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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

\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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