# Powers and Roots – Simplify an expression with roots – Exercise 1644

## Exercise

Simplify the expression:

$$\sqrt[3]{-\frac{1}{8}}+\sqrt[4]{81}-{(\frac{4}{9})}^{-\frac{1}{2}}$$

$$\sqrt[3]{-\frac{1}{8}}+\sqrt[4]{81}-{(\frac{4}{9})}^{-\frac{1}{2}}=1$$

## Solution

Using Powers and Roots rules we get:

$$\sqrt[3]{-\frac{1}{8}}+\sqrt[4]{81}-{(\frac{4}{9})}^{-\frac{1}{2}}=$$

$$=\frac{\sqrt[3]{1}}{\sqrt[3]{-8}}+\sqrt[4]{3^4}-\frac{1}{\sqrt{\frac{4}{9}}}=$$

$$=\frac{1}{-2}+3-\frac{1}{\sqrt{\frac{2^2}{3^2}}}=$$

$$=-\frac{1}{2}+3-\frac{1}{\frac{2}{3}}=$$

$$=-\frac{1}{2}+3-\frac{3}{2}=$$

$$=1$$

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