Find the value of \( (\sqrt[3]{\sqrt{0.000064}})^{5} \).

A. \( 0.0032 \)
B. \( 0.00032 \)
C. \( 0.32 \)
D. None of these

Given:

Given expression is \( (\sqrt[3]{\sqrt{0.000064}})^{5} \).
To do:

We have to find the value of \( (\sqrt[3]{\sqrt{0.000064}})^{5} \).
Solution:
 $0.000064=64\times10^{-6}$

$(\sqrt[3]{\sqrt{0.000064}})^{5}=(\sqrt[3]{\sqrt{64\times10^{-6}}})^{5}$

$=(\sqrt[3]{8\times10^{-3}})^{5}$

$=(\sqrt[3]{(2\times10^{-1})^3})^{5}$                           ($8=2^3$)

$=(2\times10^{-1})^5$

$=2^5\times10^{(-1\times5)}$

$=32\times10^{-5}$

$=0.00032$

The value of \( (\sqrt[3]{\sqrt{0.000064}})^{5} \) is $0.00032$.

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Updated on: 10-Oct-2022

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