Simplify ((x^-3y^2)^-4)/((y^6x^-4)^-2)

Problem

((x(−3)*y2)(−4))/((y6*x(−4))(−2))

Solution

1. Apply the power of a power rule to the numerator by multiplying the outer exponent −4 by the exponents of x and y inside the parentheses.

(x(−3⋅−4)*y(2⋅−4))/((y6*x(−4))(−2))

(x12*y(−8))/((y6*x(−4))(−2))

2. Apply the power of a power rule to the denominator by multiplying the outer exponent −2 by the exponents of y and x inside the parentheses.

(x12*y(−8))/(y(6⋅−2)*x(−4⋅−2))

(x12*y(−8))/(y(−12)*x8)

3. Apply the quotient rule for exponents by subtracting the exponents of like bases.

x(12−8)*y(−8−(−12))

4. Simplify the exponents to find the final values for x and y

x4*y4

Final Answer

((x(−3)*y2)(−4))/((y6*x(−4))(−2))=x4*y4

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