How do you solve the equation using properties of exponents?

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

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step-by-step explanation: