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 $16$ .

In a radical format, $8^(4/3)$ can be rewritten as a $root(3)(8^4)$ or as $(root(3)(8))^4$ . I'll do both ways.

First method: $root(3)(8^4)$ .

We would have to evaluate $8^4$ .

$root(3)(8^4)$

$=root(3)(4096)$

Now we find the cube root of 4096.

$=root(3)(4096)$

$=16$

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

The second method: $(root(3)(8))^4$ .

With $(root(3)(8))^4$ , we find the cube root of $8$ , then you quart it.

$(root(3)(8))^4$

$=2^4$

$=16$

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

Hope this helps :)