Express $(\sqrt[3]{x})^2$ in index notation. Answer ... Find the integer $n$ such that $2^n = \dfrac{1}{32}$ . Answer $n =$ ...

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Worked solution

1. Rewrite the cube root as a fractional index and simplify the power.

$(\sqrt[3]{x})^2=(x^{\frac{1}{3}})^2=x^{\frac{2}{3}}$

Answer

$x^{\frac{2}{3}}$

1. Express $\dfrac{1}{32}$ as a power of $2$ and compare indices.

Since $32=2^5$ ,
$\frac{1}{32}=\frac{1}{2^5}=2^{-5}.$
So
$2^n=2^{-5}\Rightarrow n=-5.$

Answer

$n=-5$

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