Question #06afa

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Question #06afa

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Answer 1 · 2017-06-19T00:27:51

In case of exponents, you can rewrite it as a radical and simplify it from there. In this case, it is $16$ $16$ .

Explanation:

In a radical format, $8^{\frac{4}{3}}$ $8^(4/3)$ can be rewritten as a $\sqrt[3]{8^{4}}$ $root(3)(8^4)$ or as ${(\sqrt[3]{8})}^{4}$ $(root(3)(8))^4$ . I'll do both ways.

First method: $\sqrt[3]{8^{4}}$ $root(3)(8^4)$ .

We would have to evaluate $8^{4}$ $8^4$ .

$\sqrt[3]{8^{4}}$ $root(3)(8^4)$

$= \sqrt[3]{4096}$ $=root(3)(4096)$

Now we find the cube root of 4096.

$= \sqrt[3]{4096}$ $=root(3)(4096)$

$= 16$ $=16$

It just so happens that it is a whole number (which is very convenient).

The second method: ${(\sqrt[3]{8})}^{4}$ $(root(3)(8))^4$ .

With ${(\sqrt[3]{8})}^{4}$ $(root(3)(8))^4$ , we find the cube root of $8$ $8$ , then you quart it.

${(\sqrt[3]{8})}^{4}$ $(root(3)(8))^4$

$= 2^{4}$ $=2^4$

$= 16$ $=16$

Therefore, the simplified version of $8^{\frac{4}{3}}$ $8^(4/3)$ is $16$ $16$ .

Hope this helps :)

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Question #06afa

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