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<!DOCTYPE html>
<html data-require="math expressions">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Exponent rules</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
<div class="problems">
<div id="adding">
<div class="vars" data-ensure="EXP1 !== EXP2 && EXP1 + EXP2 !== 1">
<var id="BASE">randRange(3, 9)</var>
<var id="EXP1">randRange(3, 12) * (rand(2) ? 1 : -1)</var>
<var id="EXP2">randRange(3, 12) * (rand(2) ? 1 : -1)</var>
</div>
<p class="question">
Rewrite <code>\large{<var>expr(["*", ["^", BASE, EXP1], ["^", BASE, EXP2]])</var>}</code>
in the form <code>\large{<var>BASE</var>^n}</code>.
</p>
<p class="solution" data-type="expression" data-same-form="">
<var>BASE</var>^<var>EXP1 + EXP2</var>
</p>
<div class="hints">
<p><code>\large{
<var>expr(["*", ["^", BASE, EXP1], ["^", BASE, EXP2]])</var> =
<var>expr(["^", BASE, ["+", EXP1, EXP2]])</var>}
</code></p>
<p><code>\large{\hphantom{
<var>expr(["*", ["^", BASE, EXP1], ["^", BASE, EXP2]])</var>} =
<var>BASE</var>^{<var>EXP1 + EXP2</var>}}
</code></p>
</div>
</div>
<div id="subtracting" data-type="adding">
<div class="vars" data-ensure="EXP1 !== EXP2 && EXP1 - EXP2 !== 1">
<var id="BASE">randRange(3, 9)</var>
<var id="EXP1">randRange(3, 12) * (rand(2) ? 1 : -1)</var>
<var id="EXP2">randRange(3, 12) * (rand(2) ? 1 : -1)</var>
</div>
<p class="question">
Rewrite <code>\large{<var>expr(["frac", ["^", BASE, EXP1], ["^", BASE, EXP2]])</var>}</code>
in the form <code>\large{<var>BASE</var>^n}</code>.
</p>
<p class="solution" data-type="expression" data-same-form="">
<var>BASE</var>^<var>EXP1 - EXP2</var>
</p>
<div class="hints">
<p><code>\large{
<var>expr(["frac", ["^", BASE, EXP1], ["^", BASE, EXP2]])</var> =
<var>expr(["^", BASE, ["-", EXP1, EXP2]])</var>}
</code></p>
<p><code>\large{
\hphantom{<var>expr(["frac", ["^", BASE, EXP1], ["^", BASE, EXP2]])</var>} =
<var>BASE</var>^{<var>EXP1 - EXP2</var>}}
</code></p>
</div>
</div>
<div id="multiplying" data-type="adding">
<p class="question">
Rewrite <code>\large{<var>expr(["^", ["^", BASE, EXP1], EXP2])</var>}</code>
in the form <code>\large{<var>BASE</var>^n}</code>.
</p>
<p class="solution" data-type="expression" data-same-form="">
<var>BASE</var>^<var>EXP1 * EXP2</var>
</p>
<div class="hints">
<p><code>\large{
<var>expr(["^", ["^", BASE, EXP1], EXP2])</var> =
<var>expr(["^", BASE, ["*", EXP1, EXP2]])</var>}
</code></p>
<p><code>\large{\hphantom{
<var>expr(["^", ["^", BASE, EXP1], EXP2])</var>} =
<var>BASE</var>^{<var>EXP1 * EXP2</var>}}
</code></p>
</div>
</div>
<div id="combined">
<div class="vars" data-ensure="getGCD(BASE1, BASE2) === 1">
<var id="BASE1">randRange(3, 9)</var>
<var id="BASE2">randRange(3, 9)</var>
<var id="EXP1">randRange(3, 12) * (rand(2) ? 1 : -1)</var>
<var id="EXP2">randRange(3, 12) * (rand(2) ? 1 : -1)</var>
<var id="EXP3">randRange(3, 12) * (rand(2) ? 1 : -1)</var>
</div>
<p class="question">
Rewrite <code>\large{<var>expr(["^", ["*", ["^", BASE1, EXP1], ["^", BASE2, EXP2]], EXP3])</var>}</code>
in the form <code>\large{<var>BASE1</var>^n \times <var>BASE2</var>^m}</code>.
</p>
<p class="solution" data-type="expression" data-same-form="" data-times="">
<var>BASE1</var>^<var>EXP1 * EXP3</var> * <var>BASE2</var>^<var>EXP2 * EXP3</var>
</p>
<div class="hints">
<p><code>\large{
<var>expr(["^", ["*", ["^", BASE1, EXP1], ["^", BASE2, EXP2]], EXP3])</var> =
<var>expr(["*", ["^", BASE1, ["*", EXP1, EXP3]], ["^", BASE2, ["*", EXP2, EXP3]]])</var>}
</code></p>
<p><code>\large{\hphantom{
<var>expr(["^", ["*", ["^", BASE1, EXP1], ["^", BASE2, EXP2]], EXP3])</var>} =
<var>expr(["^", BASE1, EXP1*EXP3])</var> \times <var>expr(["^", BASE2, EXP2*EXP3])</var>}
</code></p>
</div>
</div>
</div>
</div>
</body>
</html>