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

math

1 Answer
May 16, 2018

(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))