8^1/3 = 2. How?

2*2*2=8, that's how

8= 2^3
so, (8)^1/3)=(2^3)^(1/3)
=(2^(3/3))
=2

2³ = 8
2 = 8^(1/3)

OR

Logs are to base 2 in the following :-
If :-
8^(1/3) = 2
(1/3) log 8 = log 2
(1/3) (3) = log 2
1 = 1

8^(1/3) means cubed root of 8

since we want to get rid of this cubed root,we multiply it by 3
i.e
how to factorize 8 such that the power is 3,so as to get rid of the cube ,
since 2*2*2=2^3

{(2^3)^1/3}
both the 3s cancel each other and finally
2!

a^(m/n) = n√a^m

8^(1/3)
= 3√8^1 (3√ = extract the cube root)
= 3√8
= 2

Whenever you have and index of a fraction this follows;
x^m/n= nth root of x to the power m

So, in this case;
8 is x,
1 is m
and 3 is n...
Thus: 8^1/3=3rd root of 8 to the power 1
=3rd root of 8
Then; you ask your self; "What number, multiplied by it's self 3 times; is equal to 8."

Answer:2

i.e. 2x2=4
2x2x2=8

8^1/3 means cube root of 8 and thats 2 as 2*2*2=8

8^1/3 is read as cube root of 8...similiarly, 125^1/3 is the cube root of 125 which equals to 5(because cube of 5 is 5 X 5 X 5 = 125)

try not to be confused by this because in the near future u will be doing multiplication of powers XD

1. change 8 to 2^3
2. so, it'll be (2^3)^1/3 = 2
3. then, there's an exponent law that states that (x^y)^z = x^yz *you just multiply the exponent inside the parenthesis and the one outside... that is why, 2^(3/3) = 2
4. 2^1 = 2
5. 2 = 2

8^1/3 = cube root of 8