Question

How do you show that `512^(2/3) = 16^(3/2)` by using the properties of exponents?

Answer 1

`512^(2/3)`
`= (512^(1/3))^2`
`= (root(3)(512))^2`
`= 8^2`
`=64`

`16^(3/2)`
`= (16^(1/2))^3`
`= (sqrt(16))^3`
`=4^3`
`= 64`

Therefore
`512^(2/3) = 16^(3/2)`