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<!DOCTYPE html>
<html data-require="math math-format exponents">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Fractional exponents</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
<div class="exercise">
<div class="problems">
<div class="vars">
<var id="VALS">twoBasesOneRoot()</var>
<var id="BASE_N">VALS.base_1</var>
<var id="BASE_D">VALS.base_2</var>
<var id="EXP_NEG">random() &lt; 0.75</var>
<var id="EXP_D">VALS.root</var>
<!-- base, flipped if the exponent is negative. -->
<var id="BASEF_N">EXP_NEG ? BASE_D : BASE_N</var>
<var id="BASEF_D">EXP_NEG ? BASE_N : BASE_D</var>
<var id="SOL_N">round( pow( EXP_NEG ? BASE_D : BASE_N, 1 / EXP_D ) )</var>
<var id="SOL_D">round( pow( EXP_NEG ? BASE_N : BASE_D, 1 / EXP_D ) )</var>
<p class="question"><code>\Large{<var>fracParens( BASE_N, BASE_D )</var>^{^{<var>fracSmall( EXP_NEG ? -1 : 1, EXP_D )</var>}} = {?}}</code></p>
<p class="solution"><var>SOL_N / SOL_D</var></p>
<div class="hints">
<!-- Extra first step, for a question like (4/9)^(-1/2), display "=(9/4)^(1/2)" -->
<p data-if="EXP_NEG"><code>= <var>fracParens( BASEF_N, BASEF_D )</var>^{<var>fracSmall( 1, EXP_D )</var>}</code></p>
<!-- For a question like (4/9)^(1/2)... -->
<!-- "Figure out what goes in the blank: ?^2=4/9" -->
<p>Figure out what goes in the blank:<br><code>\Big(? \Big)^{<var>EXP_D</var>}=<var>frac( BASEF_N, BASEF_D )</var></code></p>
<!-- fill 2/3 into the ? -->
<p>Figure out what goes in the blank:<br><code>\Big(\color{blue}{<var>frac( SOL_N, SOL_D )</var>}\Big)^{<var>EXP_D</var>}=<var>frac( BASEF_N, BASEF_D )</var></code></p>
<!-- (4/9)^(1/2)=2/3 -->
<p data-if="EXP_NEG">So <code><var>fracParens( BASE_N, BASE_D )</var>^{<var>fracSmall( EXP_NEG ? -1 : 1, EXP_D )</var>}=<var>fracParens( BASEF_N, BASEF_D )</var>^{<var>fracSmall( 1, EXP_D )</var>}=<var>fraction( SOL_N, SOL_D, true, true, false, false )</var></code></p>
<p data-else="">So <code><var>fracParens( BASEF_N, BASEF_D )</var>^{<var>fracSmall( 1, EXP_D )</var>}=<var>fraction( SOL_N, SOL_D,true, true, false, false )</var></code></p>
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