Question

If x>0, what is the quotient of 20√ z^6/√ 16z^7 in simplest radical form?

Answer 1

I suppose you meant z > 0, or meant to use x's in place of z's…

If z > 0, then

`(20√(z^6))/(√(16z^7)) = (20√(\left(z^3\right)^2))/(√(4^2\left(z^3\right)^2z)) = (20\left|z^3\right|)/(4\left|z^3\right|√(z)) = \boxed{(5)/(√(z))}`

because

`√(z^2) = |z|`

and if z is positive, we have |z| = z, and we can eliminate common factors of z in the fraction,

`(\left|z^3\right|)/(\left|z^3\right|) = (z^3)/(z^3) = 1`