<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Quotient Rule of Exponents</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: transparent;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 16px 12px;
      user-select: none;
    }

    .header-eq {
      font-size: 22px;
      font-weight: 700;
      letter-spacing: -0.5px;
      display: flex;
      align-items: center;
      gap: 8px;
    }

    .header-eq sup {
      font-size: 14px;
      color: #0284c7;
    }

    .header-eq .denom-exp {
      color: #e11d48;
    }

    /* Main visual stage */
    .stage {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 12px 0;
      gap: 14px;
    }

    .fraction-box {
      display: flex;
      flex-direction: column;
      align-items: center;
      position: relative;
    }

    .row {
      display: flex;
      align-items: center;
      justify-content: flex-start;
      gap: 6px;
      min-height: 44px;
    }

    .fraction-bar {
      width: 100%;
      min-width: 250px;
      height: 3px;
      background: #1e2945;
      border-radius: 2px;
      margin: 2px 0;
    }

    /* Factor item */
    .factor {
      position: relative;
      width: 34px;
      height: 34px;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 20px;
      font-weight: 700;
      font-style: italic;
      border-radius: 8px;
      background: #f1f5f9;
      border: 2px solid #cbd5e1;
      color: #1e2945;
      transition: all 0.35s ease;
    }

    .dot-op {
      font-size: 14px;
      color: #94a3b8;
      font-weight: 900;
    }

    /* Slash strike-through line */
    .factor::after {
      content: '';
      position: absolute;
      width: 0;
      height: 3px;
      background: #e11d48;
      border-radius: 2px;
      top: 50%;
      left: 50%;
      transform: translate(-50%, -50%) rotate(-45deg);
      transition: width 0.35s cubic-bezier(0.34, 1.56, 0.64, 1);
    }

    /* State 2 & 3: Cancelled factors */
    .cancelled .factor.cancel {
      opacity: 0.38;
      background: #fee2e2;
      border-color: #fca5a5;
      color: #991b1b;
    }

    .cancelled .factor.cancel::after {
      width: 44px;
    }

    .cancelled .factor.remain {
      background: #e0f2fe;
      border-color: #38bdf8;
      color: #0369a1;
      box-shadow: 0 2px 8px rgba(56, 189, 248, 0.25);
    }

    /* Result callout */
    .result-row {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 10px;
      min-height: 48px;
      opacity: 0;
      transform: translateY(6px);
      transition: all 0.4s ease;
    }

    .result-row.show {
      opacity: 1;
      transform: translateY(0);
    }

    .arrow-down {
      font-size: 20px;
      color: #0284c7;
      font-weight: bold;
    }

    .result-badge {
      display: flex;
      align-items: center;
      gap: 8px;
      padding: 6px 14px;
      background: #f8fafc;
      border: 1.5px solid #0284c7;
      border-radius: 20px;
      font-size: 17px;
      font-weight: 700;
      color: #1e2945;
    }

    .result-badge span.calc {
      color: #64748b;
      font-size: 15px;
      font-weight: 600;
    }

    .result-badge span.final {
      color: #0284c7;
      font-size: 20px;
    }

    /* Interactive Stepper Navigation */
    .controls {
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 10px;
      width: 100%;
      max-width: 360px;
      margin-top: 4px;
    }

    .step-buttons {
      display: flex;
      gap: 6px;
      width: 100%;
    }

    .step-btn {
      flex: 1;
      padding: 8px 6px;
      border: 1.5px solid #cbd5e1;
      background: #ffffff;
      color: #64748b;
      border-radius: 8px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
      transition: all 0.2s ease;
    }

    .step-btn.active {
      background: #0284c7;
      border-color: #0284c7;
      color: #ffffff;
      box-shadow: 0 2px 6px rgba(2, 132, 199, 0.3);
    }

    .nav-bar {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
    }

    .nav-btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      color: #1e2945;
      width: 32px;
      height: 32px;
      border-radius: 50%;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 12px;
      cursor: pointer;
      transition: background 0.15s;
    }

    .nav-btn:hover {
      background: #e2e8f0;
    }

    .dot-indicators {
      display: flex;
      gap: 8px;
      align-items: center;
    }

    .dot {
      width: 10px;
      height: 10px;
      border-radius: 50%;
      background: #cbd5e1;
      cursor: pointer;
      border: none;
      padding: 0;
      transition: all 0.25s ease;
    }

    .dot.active {
      background: #0284c7;
      transform: scale(1.3);
    }
  </style>
</head>
<body>

  
  <div class="header-eq">
    <span>x<sup>5</sup></span>
    <span style="color:#94a3b8">/</span>
    <span>x<sup class="denom-exp">2</sup></span>
    <span>=</span>
    <span id="headerResult" style="color:#0284c7;">?</span>
  </div>

  
  <div class="stage" id="stage">
    <div class="fraction-box">
      
      <div class="row">
        <div class="factor cancel" id="num-1">x</div>
        <div class="dot-op">·</div>
        <div class="factor cancel" id="num-2">x</div>
        <div class="dot-op">·</div>
        <div class="factor remain" id="num-3">x</div>
        <div class="dot-op">·</div>
        <div class="factor remain" id="num-4">x</div>
        <div class="dot-op">·</div>
        <div class="factor remain" id="num-5">x</div>
      </div>

      <div class="fraction-bar"></div>

      
      <div class="row">
        <div class="factor cancel" id="den-1">x</div>
        <div class="dot-op">·</div>
        <div class="factor cancel" id="den-2">x</div>
      </div>
    </div>

    
    <div class="result-row" id="resultRow">
      <span class="arrow-down">↓</span>
      <div class="result-badge">
        <span>x · x · x</span>
        <span class="calc">= x<sup>5 − 2</sup> =</span>
        <span class="final">x<sup>3</sup></span>
      </div>
    </div>
  </div>

  
  <div class="controls">
    <div class="step-buttons">
      <button class="step-btn active" id="btn-0" onclick="goToStep(0)">1. Expand</button>
      <button class="step-btn" id="btn-1" onclick="goToStep(1)">2. Cancel 2</button>
      <button class="step-btn" id="btn-2" onclick="goToStep(2)">3. Count (x³)</button>
    </div>

    <div class="nav-bar">
      <button class="nav-btn" onclick="prevStep()" aria-label="Previous">◀</button>
      <button class="nav-btn" id="playBtn" onclick="togglePlay()" aria-label="Play/Pause">⏸</button>
      <div class="dot-indicators">
        <button class="dot active" id="dot-0" onclick="goToStep(0)" aria-label="Step 1"></button>
        <button class="dot" id="dot-1" onclick="goToStep(1)" aria-label="Step 2"></button>
        <button class="dot" id="dot-2" onclick="goToStep(2)" aria-label="Step 3"></button>
      </div>
      <button class="nav-btn" onclick="nextStep()" aria-label="Next">▶</button>
    </div>
  </div>

  <script>
    let currentStep = 0;
    let isPlaying = true;
    let timer = null;
    const TOTAL_STEPS = 3;
    const STEP_DURATION = 3200;

    const stage = document.getElementById('stage');
    const resultRow = document.getElementById('resultRow');
    const headerResult = document.getElementById('headerResult');
    const playBtn = document.getElementById('playBtn');

    function updateUI() {
      // Update Buttons & Dots
      for (let i = 0; i < TOTAL_STEPS; i++) {
        const btn = document.getElementById('btn-' + i);
        const dot = document.getElementById('dot-' + i);
        if (btn) btn.classList.toggle('active', i === currentStep);
        if (dot) dot.classList.toggle('active', i === currentStep);
      }

      // Step-specific visual states
      if (currentStep === 0) {
        stage.classList.remove('cancelled');
        resultRow.classList.remove('show');
        headerResult.innerHTML = '?';
      } else if (currentStep === 1) {
        stage.classList.add('cancelled');
        resultRow.classList.remove('show');
        headerResult.innerHTML = 'x<sup>5−2</sup>';
      } else if (currentStep === 2) {
        stage.classList.add('cancelled');
        resultRow.classList.add('show');
        headerResult.innerHTML = 'x<sup>3</sup>';
      }
    }

    function goToStep(stepIndex) {
      currentStep = (stepIndex + TOTAL_STEPS) % TOTAL_STEPS;
      updateUI();
      if (isPlaying) {
        resetTimer();
      }
    }

    function nextStep() {
      goToStep(currentStep + 1);
    }

    function prevStep() {
      goToStep(currentStep - 1);
    }

    function togglePlay() {
      isPlaying = !isPlaying;
      playBtn.textContent = isPlaying ? '⏸' : '▶';
      if (isPlaying) {
        resetTimer();
      } else {
        clearInterval(timer);
      }
    }

    function resetTimer() {
      clearInterval(timer);
      timer = setInterval(() => {
        currentStep = (currentStep + 1) % TOTAL_STEPS;
        updateUI();
      }, STEP_DURATION);
    }

    // Initialize Auto-play
    updateUI();
    resetTimer();
  </script>
</body>
</html>

Product and Quotient Rules of Exponents

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    }
    body {
      background: #ffffff;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }
    .diagram-content {
      width: 100%;
      max-width: 520px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 16px;
    }
    /* Mode Selector */
    .pill-nav {
      display: flex;
      gap: 6px;
      background: #f1f5f9;
      padding: 4px;
      border-radius: 9999px;
      border: 1px solid #e2e8f0;
    }
    .pill-btn {
      border: none;
      background: transparent;
      padding: 6px 14px;
      border-radius: 9999px;
      font-size: 14px;
      font-weight: 600;
      color: #64748b;
      cursor: pointer;
      transition: all 0.2s ease;
    }
    .pill-btn.active {
      background: #ffffff;
      color: #1e2945;
      box-shadow: 0 1px 3px rgba(0,0,0,0.1);
    }

    /* Main Display Area */
    .expression-stage {
      width: 100%;
      display: grid;
      grid-template-columns: 1fr auto 1fr;
      align-items: center;
      gap: 8px;
      padding: 8px 0;
    }
    .callout {
      padding: 10px 12px;
      border-radius: 10px;
      font-size: 13px;
      line-height: 1.3;
      transition: all 0.2s ease;
    }
    .callout-title {
      font-weight: 700;
      font-size: 13px;
      margin-bottom: 2px;
    }
    .callout-desc {
      font-size: 12px;
      opacity: 0.9;
    }
    .callout-base {
      background: #eff6ff;
      border: 1px solid #bfdbfe;
      color: #1d4ed8;
      text-align: right;
    }
    .callout-exp {
      background: #ecfdf5;
      border: 1px solid #a7f3d0;
      color: #047857;
      text-align: left;
    }
    .math-hero {
      display: flex;
      align-items: baseline;
      justify-content: center;
      font-family: "Cambria Math", "Times New Roman", serif;
      padding: 0 10px;
      user-select: none;
    }
    .base-symbol {
      font-size: 64px;
      font-weight: 700;
      font-style: italic;
      color: #2563eb;
      line-height: 1;
      padding: 4px 6px;
      border-radius: 8px;
      transition: background-color 0.2s;
    }
    .exp-symbol {
      font-size: 38px;
      font-weight: 700;
      font-style: italic;
      color: #059669;
      line-height: 1;
      vertical-align: super;
      transform: translateY(-24px);
      padding: 2px 4px;
      border-radius: 6px;
      transition: background-color 0.2s;
    }

    /* Flow connector */
    .flow-arrow {
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 2px;
      color: #94a3b8;
      font-size: 12px;
      font-weight: 600;
      text-transform: uppercase;
      letter-spacing: 0.05em;
    }
    .arrow-icon {
      font-size: 16px;
      line-height: 1;
      color: #64748b;
    }

    /* Expansion Card */
    .expansion-card {
      width: 100%;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 16px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 8px;
      box-shadow: 0 1px 3px rgba(0,0,0,0.03);
    }
    .expansion-row {
      display: flex;
      align-items: center;
      justify-content: center;
      flex-wrap: wrap;
      gap: 6px;
      font-family: "Cambria Math", "Times New Roman", serif;
      font-size: 24px;
      font-style: italic;
      font-weight: 600;
      color: #1e2945;
      min-height: 38px;
    }
    .factor-item {
      color: #2563eb;
      background: #eff6ff;
      border: 1px solid #dbeafe;
      border-radius: 6px;
      padding: 2px 8px;
      display: inline-flex;
      align-items: center;
      justify-content: center;
    }
    .dot-sep {
      color: #94a3b8;
      font-style: normal;
      font-weight: bold;
    }
    .bracket-label {
      font-size: 13px;
      font-weight: 600;
      color: #059669;
      background: #ecfdf5;
      border: 1px solid #a7f3d0;
      padding: 3px 12px;
      border-radius: 9999px;
      display: flex;
      align-items: center;
      gap: 4px;
    }

    @media (max-width: 420px) {
      .expression-stage {
        grid-template-columns: 1fr;
        gap: 10px;
      }
      .callout {
        text-align: center !important;
      }
      .math-hero {
        order: -1;
      }
      .base-symbol {
        font-size: 52px;
      }
      .exp-symbol {
        font-size: 32px;
        transform: translateY(-20px);
      }
      .expansion-row {
        font-size: 20px;
      }
    }
  </style>
</head>
<body>
  <div class="diagram-content">
    
    <div class="pill-nav" role="tablist">
      <button class="pill-btn active" onclick="setMode(0)" role="tab">General aⁿ</button>
      <button class="pill-btn" onclick="setMode(1)" role="tab">2⁴</button>
      <button class="pill-btn" onclick="setMode(2)" role="tab">x³</button>
      <button class="pill-btn" onclick="setMode(3)" role="tab">5²</button>
    </div>

    
    <div class="expression-stage">
      <div class="callout callout-base">
        <div class="callout-title">Base (<span id="baseName">a</span>)</div>
        <div class="callout-desc">The factor being multiplied</div>
      </div>

      <div class="math-hero">
        <span class="base-symbol" id="heroBase">a</span>
        <span class="exp-symbol" id="heroExp">n</span>
      </div>

      <div class="callout callout-exp">
        <div class="callout-title">Exponent (<span id="expName">n</span>)</div>
        <div class="callout-desc">How many factors to multiply</div>
      </div>
    </div>

    
    <div class="flow-arrow">
      <span class="arrow-icon">↓</span>
      <span>Expanded Form</span>
    </div>

    
    <div class="expansion-card">
      <div class="expansion-row" id="expansionRow">
        
      </div>
      <div class="bracket-label" id="bracketTag">
        <span>⏡</span>
        <span id="bracketText">n factors of a</span>
      </div>
    </div>
  </div>

  <script>
    const data = [
      {
        base: 'a',
        exp: 'n',
        factors: ['a', 'a', 'a', '...', 'a'],
        tag: 'n factors of a'
      },
      {
        base: '2',
        exp: '4',
        factors: ['2', '2', '2', '2'],
        tag: '4 factors = 16'
      },
      {
        base: 'x',
        exp: '3',
        factors: ['x', 'x', 'x'],
        tag: '3 factors of x'
      },
      {
        base: '5',
        exp: '2',
        factors: ['5', '5'],
        tag: '2 factors = 25'
      }
    ];

    function setMode(idx) {
      const btns = document.querySelectorAll('.pill-btn');
      btns.forEach((b, i) => b.classList.toggle('active', i === idx));

      const item = data[idx];
      document.getElementById('heroBase').textContent = item.base;
      document.getElementById('heroExp').textContent = item.exp;
      document.getElementById('baseName').textContent = item.base;
      document.getElementById('expName').textContent = item.exp;
      document.getElementById('bracketText').textContent = item.tag;

      const row = document.getElementById('expansionRow');
      row.innerHTML = '';
      item.factors.forEach((f, i) => {
        const span = document.createElement('span');
        span.className = 'factor-item';
        span.textContent = f;
        row.appendChild(span);

        if (i < item.factors.length - 1) {
          const dot = document.createElement('span');
          dot.className = 'dot-sep';
          dot.textContent = ' · ';
          row.appendChild(dot);
        }
      });
    }

    // Initialize with general form
    setMode(0);
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Product Rule of Exponents</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 16px 12px;
      gap: 16px;
    }

    .equation-header {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      font-size: 26px;
      font-weight: 800;
      letter-spacing: -0.5px;
    }

    .term-blue {
      color: #0284c7;
      background: #e0f2fe;
      padding: 4px 12px;
      border-radius: 8px;
      border: 1.5px solid #bae6fd;
    }

    .term-purple {
      color: #7c3aed;
      background: #f3e8ff;
      padding: 4px 12px;
      border-radius: 8px;
      border: 1.5px solid #e9d5ff;
    }

    .op {
      color: #64748b;
      font-size: 24px;
      font-weight: 700;
    }

    .visual-flow {
      display: flex;
      flex-direction: column;
      align-items: center;
      width: 100%;
      max-width: 580px;
      gap: 12px;
    }

    .factors-row {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      width: 100%;
      flex-wrap: wrap;
    }

    .factor-card {
      background: #f8fafc;
      border-radius: 12px;
      padding: 12px 14px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 6px;
      flex: 1 1 140px;
      max-width: 220px;
      min-width: 130px;
      border: 1.5px solid #e2e8f0;
      transition: box-shadow 0.2s ease;
    }

    .factor-card.blue {
      border-color: #7dd3fc;
      background: #f0f9ff;
    }

    .factor-card.purple {
      border-color: #d8b4fe;
      background: #faf5ff;
    }

    .factor-card.combined {
      border-color: #86efac;
      background: #f0fdf4;
      max-width: 100%;
      width: 100%;
      flex: 1 1 100%;
      padding: 14px;
    }

    .factor-expr {
      font-size: 19px;
      font-weight: 700;
      letter-spacing: 0.5px;
      font-family: "SF Pro Text", "Segoe UI", system-ui, sans-serif;
      text-align: center;
    }

    .factor-expr .b-part { color: #0284c7; }
    .factor-expr .p-part { color: #7c3aed; }
    .factor-expr .dot-sep { color: #94a3b8; margin: 0 1px; }

    .badge {
      font-size: 12px;
      font-weight: 700;
      padding: 3px 10px;
      border-radius: 20px;
      text-transform: uppercase;
      letter-spacing: 0.5px;
    }

    .badge-blue {
      background: #0284c7;
      color: #ffffff;
    }

    .badge-purple {
      background: #7c3aed;
      color: #ffffff;
    }

    .badge-green {
      background: #16a34a;
      color: #ffffff;
    }

    .arrow-down {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      color: #64748b;
      font-size: 13px;
      font-weight: 700;
    }

    .arrow-down span {
      font-size: 18px;
    }

    .result-math {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      font-size: 19px;
      font-weight: 800;
      color: #1e2945;
      margin-top: 2px;
      flex-wrap: wrap;
    }

    .result-math .highlight {
      color: #16a34a;
      background: #dcfce7;
      padding: 2px 10px;
      border-radius: 6px;
      border: 1px solid #bbf7d0;
    }

    .rule-pill {
      display: inline-flex;
      align-items: center;
      gap: 6px;
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      padding: 6px 16px;
      border-radius: 999px;
      font-size: 14px;
      font-weight: 700;
      color: #334155;
    }

    sup {
      font-size: 0.7em;
      line-height: 0;
      position: relative;
      vertical-align: baseline;
      top: -0.5em;
    }
  </style>
</head>
<body>

  
  <div class="equation-header">
    <span class="term-blue">x<sup>3</sup></span>
    <span class="op">·</span>
    <span class="term-purple">x<sup>4</sup></span>
  </div>

  <div class="visual-flow">
    
    <div class="factors-row">
      <div class="factor-card blue">
        <div class="factor-expr b-part">x · x · x</div>
        <span class="badge badge-blue">3 factors</span>
      </div>

      <span class="op">·</span>

      <div class="factor-card purple">
        <div class="factor-expr p-part">x · x · x · x</div>
        <span class="badge badge-purple">4 factors</span>
      </div>
    </div>

    
    <div class="arrow-down">
      <span>↓</span> combine all factors
    </div>

    
    <div class="factor-card combined">
      <div class="factor-expr">
        (<span class="b-part">x · x · x</span><span class="dot-sep"> · </span><span class="p-part">x · x · x · x</span>)
      </div>
      <div class="result-math">
        <span>= x<sup><span style="color:#0284c7">3</span>+<span style="color:#7c3aed">4</span></sup></span>
        <span>=</span>
        <span class="highlight">x<sup>7</sup></span>
      </div>
      <span class="badge badge-green" style="margin-top:4px;">7 total factors</span>
    </div>
  </div>

  
  <div class="rule-pill">
    <span>Rule:</span>
    <span>x<sup>m</sup> · x<sup>n</sup> = x<sup>m+n</sup></span>
  </div>

</body>
</html>

OGM.9.NS.3

Aligned learning resources

Related diagrams