Question - Finding the Value of an Exponent

Given the equation:

$$9^{2m - 5} \times 9^3 = 9^{m + 1}$$

Combine the left-hand side using the property of exponents:

$$9^{(2m - 5) + 3} = 9^{m + 1}$$

This simplifies to:

$$9^{2m - 2} = 9^{m + 1}$$

Since the bases are the same, set the exponents equal:

$$2m - 2 = m + 1$$

Isolate \( m \):

$$2m - m = 1 + 2$$

$$m = 3$$