Question

How do I solve for m?

Answer 1

$x^3y^2\left(\dfrac{x^2 y^3 z^m}{z^{-5}}\right)=x^5y^5z\\\\ x^5y^5z^{m+5}=x^5y^5z\\\\ m+5=1\\\\ \boxed{m=-4}$

Answer 2

Step One

Bring z^(-5) to the numerator.

x^3y^2(x^2 y^3 z^(m + 5)) = x^5 * 5y^5 * z

Step Two

Remove the brackets on the left

x^(3 + 2) * y ^ (2 + 3) * z^(m + 5) = x^5 * y^5 * z

x^5 * y^5  * z^(m + 5) = x^5 * y^5 * z                     Divide by x^5 * y^5

z ^(m + 5) = z^1                                       Since the bases are the same, you can equate the powers.

m + 5 = 1                                                 Subtract 5

m = 1 - 5

m = - 4     <<<< Answer