Question

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

Answer 1

`\large\boxed{x^(-10)y^8=(y^8)/(x^(10))}`

Explanation:

`\left((x^(-4)y)/(x^(-9)y^5)\right)^(-2)\qquad\text{use}\ (a^n)/(a^m)=a^(n-m)\\\\\left(x^(-4-(-9))y^(1-5)\right)^(-2)=(x^5y^(-4))^(-2)\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^(nm)\\\\=(x^5)^(-2)(y^(-4))^(-2)=x^((5)(-2))y^((-4)(-2))=x^(-10)y^8\qquad\text{use}\ a^(-n)=(1)/(a^n)\\\\=(y^8)/(x^(10))`