Question

How do you simplify `(64/9)^(3/2)`?

Answer 1

`(64/9)^(3/2)=sqrt((64/9)^3)`

`=sqrt(262144/729)`

`=512/27`

Answer 2

`(512)/(27)`

Explanation:

Simplify
`((64)/(9))^((3)/(2))`

This fractional exponent means to find the square root of the numbers raised to the third power.

`sqrt(((64)/(9))^3`

1) Find the square roots of the numbers
`((8)/(3))^3`

2) Raise the numbers to the third power
`(512)/(27)`

`Answer`
`(512)/(27)`

Here's a Khan Academy video about evaluating rational exponents:
https://www.khanacademy.org/math/algebra/rational-exponents-and-radicals/alg1-rational-exp-eval/v/fractional-exponents-with-numerators-other-than-1