Question

How do you solve the equation using properties of exponents?

Answer 1

You are solving for exponent m. Note the equal sign. What you do to one side, you do to the other.

First, divide x^3 and y^2 from both sides

x^(3 - 3) * y^(2 - 2) * ((x² * y³ * z^m)/(z^-5)) = (x^5 - 3)(y^5 - 2)(z)

(x² * y³ * z^m)/(z^-5) = (x²)(y³)(z)

Next, flip z^-5 to the numerator

(x² * y³ *z^(m + 5)) = (x²)(y³)(z)

Simplify the z

x² - x² = 0

y³ - y³ = 0

z^(m + 5) = z

z^ (-4 + 5) = z

z^1 = z

m = -4

hope this helps