Question

Simplify the expression (8/125) ^1/3

Answer 1

Answer: 2/5

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Work Shown:

(8/125)^(1/3) = (8^(1/3))/(125^(1/3))
(8/125)^(1/3) = ((2^3)^(1/3))/((5^3)^(1/3))
(8/125)^(1/3) = (2^(3*(1/3)))/(5^(3*(1/3)))
(8/125)^(1/3) = (2^(3/3))/(5^(3/3))
(8/125)^(1/3) = (2^1)/(5^1)
(8/125)^(1/3) = 2/5

In short, we take the cube root of each piece
The cube root of 8 is 2
The cube root of 125 is 5
That's why the cube root of (8/125) is 2/5