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

Exercise

Simplify the expression:

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

Final Answer

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Solution

Using Powers and Roots rules we get:

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

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

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

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

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

$=1$