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yawa3891 [41]
2 years ago
11

frac{1}{4}" alt="(\frac{1}{81})^\frac{1}{4}" align="absmiddle" class="latex-formula">

Its asking me to put this expression into radical form.
Mathematics
1 answer:
Oksanka [162]2 years ago
4 0

If n>1, we write x^{1/n}=\sqrt[n]x. So

\left(\dfrac1{81}\right)^{1/4}=\sqrt[4]{\dfrac1{81}}

We can simplify this further by using properties of square roots:

\sqrt{\dfrac ab}=\dfrac{\sqrt a}{\sqrt b}\implies\sqrt[4]{\dfrac1{81}}=\dfrac{\sqrt[4]1}{\sqrt[4]{81}}=\dfrac1{\sqrt[4]{81}}

Next, 81=9^2=(3^2)^2=3^4, and so \sqrt[4]{81}=\sqrt[4]{3^4}=3, so

\left(\dfrac1{81}\right)^{1/4}=\dfrac13

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