Question

How do you simplify `(x^(5/3)y)/(xy^(-1/2))`?

Answer 1

`color(green)(x^(2/3)y^(3/2))`

Explanation:

`(x^(5/3)y)/(xy^(-1/2))`
`color(white)("XXX")=(x^(5/3))/(x) * (y)/(y^(-1/2))`

`color(white)("XXX")=(x^(5/3) * x^(-1)) * (y * y^(1/2))`

`color(white)("XXX")=x^(2/3) * y^(3/2)`

Answer 2

Just for comparison to Alan's

`color(maroon)(x^(2/3)y^(3/2))`

Explanation:

Given:`" "(x^(5/3)y)/(xy^(-1/2))`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Write as: `" "(root(3)(x^3xx x^2)color(white)(..)ysqrt(y))/x`

`" "(cancel(x)^1root(3)(x^2)color(white)(..)ysqrt(y))/(cancel(x)^1`

`root(3)(x^2) xx sqrt(y^2xxy)`

`x^(2/3)xxy^(3/2)`

`x^(2/3)y^(3/2)`