Math problem : Simplify 125 ^ -2/3?

Question

This problem is 125 and then its cubed -2/3

Answer 1

125=5^3
therefore 125^(-2/3)= 5^(3*-2/3)
=5^-2
=1/(5^2)
=1/25
0.04

Answer 2

= 1 / (125)^(2/3)
= 1 / 5² (after taking cube root of 125)
= 1 / 25

Answer 3

1/25
You have to see that the -2/3 exponent accomplishes a couple of things. It puts 125 under the fraction bar so that the number is 1/125. then what you are going to do to the 125 is take it's cube root, yes, because 3 is the denominator in that exponent. but also you are going to square whatever that result is because 2 is the numerator in that exponent.
so look at what the negative sign in the exponent does - makes it the denominator of a fraction with 1 as numerator.
look at what the denominator of the exponent does. It shows whether you are taking a square root, a cube root, etc.
look at what the numerator of the exponent does. It takes whatever the result of that square root or cube root or whatever is and raises it to a power.
all of it ends up being 1/something.

Answer 4

It's been a while since .... but the 1/3 is cube root so that's 5 and then 2 is square so that's 25 and then the - is inverse so that's 1/25 or 4/100 or 4% or 0.04

Answer 5

the 2/3 exponent menas take the cube root and square it
the negative exponent means the reciprocal so the problem is
1/125^2/3 = 1/5^2= 1/25 = .04

Answer 6

Answer is 1/25 or 0.04.

125^(-2/3) means the reciprocal of the cube root of 125 squared.

125 squared = 15,625
cube root of 15,625 = 25
reciprocal of 25 = 1/25 or 0.04

Answer 7

125 ^ -2/3
= (5^3)^-2/3
= 5^-2 = 1/5^2 = 1/25 = .04

Answer 8

125 ^ (-2/3)
= 1/ [125 ^ (2/3)]
= 1/ [125 ^ (1/3)]^2
= 1/ [cuberoot(125)]^2
= 1/ 5^2
= 1/25
= 0.04

Answer 9

125 ^(-2/3)
(125^(1/3) ) ^-2
5^-2
1/5^2
1/25

Answer 10

=1/(125)^2/3
=1/(125^(1/3))^2
1/25