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What is the simplified expression of ³(the square root of)64⁶ ?

1 Answer

Jun 20, 2018

$64^{2} = 4096$ $64 ^ 2 = 4096$

Explanation:

This question becomes easy if you remember that extracting the $n$ $n$ -th root is the same as raising to the $\frac{1}{n}$ $1/n$ -th power.

So, $\sqrt[3]{64^{6}} = {(64^{6})}^{\frac{1}{3}}$ $\root[3]{64^6} = (64^6)^{1/3}$

Now use the formula ${(a^{b})}^{c} = a^{b c}$ $(a^b)^c = a^{bc}$ to get

$64^{6 \cdot \frac{1}{3}} = 64^{2}$ $64^(6*1/3) = 64 ^ 2$

In case you need it, $64^{2} = 4096$ $64^2=4096$

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