Apply the product rule of integer exponents to find the numerical equivalent of 12^-5 x 12^7.

Show your work and explain how you used the product rule of integer exponents.

1 answer

To apply the product rule of integer exponents, we need to multiply the bases (12) together and add the exponents (-5 and 7) together.

The product rule states that for any positive integers m and n, and any real number a, a^m * a^n = a^(m+n).

In this case, we have 12^(-5) * 12^7.

Multiplying the bases 12 * 12 gives us 144.

Adding the exponents -5 + 7 gives us 2.

Therefore, 12^(-5) * 12^7 = 144^2.

To find the numerical value of 144^2, we simply square 144.

144^2 = 20,736.

So, the numerical equivalent of 12^-5 * 12^7 is 20,736.