How do you simplify (x^(-1/2)y^2)^(-5/4)/(x^2y^(1/2)?

1 Answer
May 3, 2017

f(x,y) = frac(1)(x^(11/8)y^3)

Explanation:

Given:
f(x,y) =frac((x^(-1/2)y^2)^(-5/4))(x^2y^(1/2))

We first distribute the power in the numerator using the Power Rule for exponents, since the base terms x and y are being multiplied together and not added.

f(x,y) =frac(x^((-1/2)(-5/4))y^((2)(-5/4)))(x^2y^(1/2)) = frac(x^(5/8)y^(-5/2))(x^2y^(1/2))

Now we apply the Quotient Rule for Exponents on both x and y, following:

x^a/x^b = x^(a-b)

f(x,y) = x^(5/8-2)y^(-5/2-1/2) = x^(-11/8)y^(-3)

Now, we apply the negative exponent rule,

x^(-a) = 1/x^(a)

f(x,y) =1/(x^(11/8)y^(3))