Fractions in exponent?

Question

I've done this before, but I need a little refresher. Tonight.

I remember something about root vs. exponent, but not how it works.

Basically, I have (8x^3)^2/3

I hope that's clear.

Answer 1

(8x³)^(2/3) = 8^(2/3) x^(2/3) = 4(x^2/3)

Answer 2

Basically the 2/3 means to square the number, then take the cube root.

In your case, you multiply the exponent inside your brackets by the external exponent, so 3 *(2/3) = 6/3 = 2 and your end result is 8x^2.

The numerator in an exponent squares/cubes the number etc, and the denominator takes the square-/cube-root. Obviously square and cube refer to when the numbers 2 or 3 appear - extend the analogy for different numerals!!

Answer 3

That's like... eight x cubed whole raised to two thirds right? That is, in other words cube root of ((eight times x cubed)
Basically you deal with the numerator like you would with an integer exponent, and the denominator, say its p, means you take the pth root of the thing...8^(1/3)=2.

All the best! It's a little tough to explain it here it may be tougher to understand.

Answer 4

What you have is: [8*(x^3)]^2/3 or a product of two nos. 8 and (x^3) raised to a power, 2/3. Each of the factors is then raised to the 2/3. So we get 8^2/3 and (x^3)^2/3.
8^2/3 is the same as (8^1/3)^2 = 2^2 =4
(x^3)^2/3 is the same as [(x^3)^1/3]^2 or x^2
The answer is then 4x^2