Simplifying exponential equation help

x^(2/3) * ( 8x)^(1/3)   =

x^(2/3) * 2x^(1/3)  =

x^(2/3) * x^(1/3) * 2  =

x * 2  =

2x

I'm going to guess you were saying \(x^{\frac{2}{3}}\times(8x)^{\frac{1}{3}}\)

I've done some exploration of exponents on my own, and discovered a few rules I otherwise would be oblivious to. So, let's start by making the first term have a unit fraction (that is, one over something, or no fraction): \((x^{2})^{\frac{1}{3}}*(8x)^{\frac{1}{3}}\)

One of those rules is that the reciprocal power x of a number y = the xth root of y.

Another is that you can multiply bases w/ the same powers.

\(\sqrt[3]{x^2\times8x}\)

The most simple form can be found by multiplying the stuff under the same power, so:

\(\sqrt[3]{8x^3}\)

This one is even easier to simplify. 8 = 2³, so:

\(2x\)

is the answer.