Question

Apply the product rule of intiger exponents to find the numerical equivalent of 12^-5•12^7. Show your work and explain how you used the product rule of intiger exponents.

Answer 1

The product rule of integer exponents states that when multiplying two terms with the same base, we add their exponents.

To find the numerical equivalent of 12^-5 • 12^7, we can first apply the product rule to simplify the expression.

12^-5 • 12^7 = 12^(-5 + 7)

Since the bases are the same (12), we add the exponents (-5 + 7) which gives us 12^2.

Therefore, 12^-5 • 12^7 is numerically equivalent to 12^2.

To calculate 12^2, we multiply 12 by itself:

12^2 = 12 × 12 = 144.

Hence, the numerical equivalent of 12^-5 • 12^7 is 144.