Question

Simplify each of the following removing radical signs and negative indices wherever they occur
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Answer 1

Given  :    $\sqrt{4} ^{\frac{-3}{4} }$

$\frac{1}{\sqrt[3]{4^{-5}} }$

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

To Find : Simplify each of the following removing radical signs and negative indices

Solution:

$\sqrt{4} ^{\frac{-3}{4} }$

$=\sqrt{2^2} ^{\frac{-3}{4} }$

$=2^{\frac{-3}{4} }$

$=\dfrac{1}{2^{\frac{3}{4} }}$

$\dfrac{1}{\sqrt[3]{4^{-5}} }$

$= \dfrac{1}{ {4^{\frac{-5}{3} }} }$

$= 4^{\frac{5}{3}$

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

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

$=2^{\frac{-1}{2} }$

$= \dfrac{1}{2^{\frac{1}{2} }}$

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