Why does 8^(2 / 3) = 4?

Question

I mean to say, I forget how to do this basic math and arrive at 4.

Answer 1

8^(2/3) = (cubed root of 8)^2
= (2)^2
= 4

or
8^(2/3) = cubed root of (8^2)
= cubed root of 64
= 4

Either way it doesn't matter.

Answer 2

Basically, the math goes like this:

8 to the (2/3), you change it to root form in which the numerator of 2 goes on the inside of the square root and the denominator goes on the outside of the square root to make it a cube root. Therefore,

(8)^2 = 8 X 8 = 64
64 to the cube root of 3 = so which number multiplied 3
times will give you 64?

The answer:
4x4x4 = 64

Therefore, the cube root of 64 = 4.

I hope this was helpful, for more explanation look up
rational exponents in a pre-calculus book.

Answer 3

There are two ways to think of it. Each has been mentioned by others already, but no-one has gotten them both.

The basic idea is that raising a number to the power of 2 is squaring it, while raising it to the power of 1/3 is taking the cube root. You could take the cube root first. The cube root of 8 is 2. Then square the answer, and you get 2^2 = 4.

You could also square it first, getting 8^2 = 64. Then take the cube root of 64, which is 4.

Either way you get the same answer.

Answer 4

OK!

8^(2/3) = (2^3) ^ (2) ^ (1/3)
The third power and cube root cancel, leaving:
2^2 =4

Alternatively:

8^(2/3) = 8^2 ^(1/3)= 64^(1/3) = (4*4*4)^(1/3)= 4

Done!

Answer 5

8^(2/3) is the same as (8^2) ^ (1/3)... the cube root of 8², right?
8² is 64. The cube root of that is 4, since 4^3 is 64.

Answer 6

42 2/3 (42.6666666666666666666)

8^(2/3) is 8 to the 2/3 power, which is the same as 8 times 2/3 of its self. (as 8 to the 2 power is 8*8) 2/3 of 8 is 5 1/3. 8 times 5 1/3 is 42 2/3, not 4

Answer 7

8²/³ is the same that ³\/8² . So,
³\/8² = 4 =>
³\/(2³)² = Cancelling radical =>
2² = 4
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Answer 8

Why does 8^(2 / 3) = 4

= (2^3)^2/3 = 2^(3*2/3) = 2^2 = 4

In general,(x^m)^n = x ^m*n

Answer 9

see,we can writ 8 as 2^3 since 2 x 2x 2=8
the expression becomes
(2^3)^2/3=4
(a^m)^n=a^m x n[law of exponent]
2^3 x(2/3)=4
2^(6/3)=4
2^2=4
4=4
hence proved

Answer 10

the numerator (2 in this problem)becomes the power
the denominator(3 in this problem) becomes the root

so ,
cube root of 8^2
cube root of 64 = 4...
there u go
Hope this helps