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# Simplifying exponential equation help

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X^2/3(8x)^1/3

thanks!

Guest May 18, 2017
#1
+87301
+2

x^(2/3) * ( 8x)^(1/3)   =

x^(2/3) * 2x^(1/3)  =

x^(2/3) * x^(1/3) * 2  =

x * 2  =

2x

CPhill  May 18, 2017
#3
0

Thanks

Guest May 19, 2017
#2
+541
+3

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:

$$2x$$

helperid1839321  May 18, 2017
#4
+1

Much help thanks very much

Guest May 19, 2017