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

math

1 Answer
Mr. Hsia
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))#

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