Which expression is equivalent to (x^-4 y / x^-9 y^5) ^2

y^12 x^10

Step-by-step explanation:

Simplify the following:

((y y^5) / (x^4 x^ (-9))) ^2

Multiply the numerator of y/x^ (-9) by the reciprocal of the denominator. y/x^ (-9) = y x^9:

((y x^9 y^5) / (x^4)) ^2

Combine powers. (y x^9 y^5) / x^4 = y^ (5 + 1) x^ (9 - 4):

(y^ (5 + 1) x^ (9 - 4)) ^2

5 + 1 = 6:

(y^6 x^ (9 - 4)) ^2

9 - 4 = 5:

(y^6 x^5) ^2

Multiply each exponent in y^6 x^5 by 2:

y^ (2*6) x^ (2*5)

2*5 = 10:

y^ (2*6) x^10

2*6 = 12:

Answer: y^12 x^10