<p>Rewrite each of the following in radical form and hence evaluate the results without using a calculator.</p>
<ol class="i-list"><li><div class="list-item-paragraph">${{81}^{\frac{1}{4}}}$</div></li><li><div class="list-item-paragraph">${{8}^{-\frac{1}{3}}}$</div></li></ol>
<p>In general, if $m$ and $n$ are positive integers,</p>
<p style="text-align: center">${{a}^{\frac{m}{n}}}=\sqrt[n]{{{a}^{m}}}$ or ${{\left( \sqrt[n]{a} \right)}^{m}}$</p>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765784425067-1bfbdatst5u.png" style="max-width: 100px; height: auto; display: block;" class="aligncenter custom-width" /></figure>
<p>if $a>0$.</p>

Rewrite each of the following in radical form and hence evaluate the results without using a calculator.

In general, if $m$ and $n$ are positive integers,

${{a}^{\frac{m}{n}}}=\sqrt[n]{{{a}^{m}}}$ or ${{\left( \sqrt[n]{a} \right)}^{m}}$

From Indices to Radicals: Understanding Fractional Powers

From Indices to Radicals: Understanding Fractional Powers

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