Apply the product rule of Integer Exponents to find the numerical equivalent of 12^-5 * 12^7 show your work and explain how you used the product rule of Integer Exponents ???

Answer 1

To apply the product rule of Integer Exponents, we need to add the exponents when multiplying two terms with the same base.

For the expression 12^-5 * 12^7, we can use the product rule of Integer Exponents to combine the terms. The rule states that when multiplying two terms with the same base, we can add the exponents:

12^-5 * 12^7 = 12^(-5 + 7)

Now, let's simplify the exponent:

12^(-5 + 7) = 12^2

Therefore, the expression 12^-5 * 12^7 is equal to 12^2.

To find the numerical equivalent, we can evaluate 12^2:

12^2 = 12 * 12 = 144

Therefore, the numerical equivalent of 12^-5 * 12^7 is 144.