Question

What is the answer to (x^3y^-2)^(1/2) / (x^-5y)^(-1/2) ?

math

Answer 1

`(x^4)/(y^(3/2))`

Explanation:

`(((x^3)(y^-2))^(1/2)) / (((x^-5)(y))^(1/2))`

Power of Power & Power of Product Properties: Multiply Outside exponent with each exponent inside the ( )
`= ((x^(3/2))(y^(-1))) / ((x^(-5/2))(y^(1/2))`

Power of Quotient: For like Bases, Subtract Top Exponent with Bottom Exponent
`= (x^((3/2)-(-5/2)))(y^((-1)-(1/2)))`
`= (x^(8/2))(y^(-3/2))`

Negative Exponent means Base is moved to denominator
`= (x^4)/(y^(3/2))`