Apply the product rule of integer exponents to find the numerical equivalent of 12−5⋅127 . 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 multiply the base numbers and then apply the exponent to the product.

Here, the base number is 12 and the exponent is -5.

First, let's rewrite the expression using the product rule of integer exponents:
12^(-5) * 127

According to the product rule, we multiply the base numbers, so let's calculate 12^(-5) first:
12^(-5) = 1 / 12^(5)

Now, we can substitute this value back into our expression:
(1 / 12^(5)) * 127

To find the numerical equivalent, we need to evaluate this expression:
1 / 12^(5) = 1 / (12 * 12 * 12 * 12 * 12) = 1 / 248,832

Finally, we multiply the result by 127:
(1 / 248,832) * 127 = 0.000508 [rounded to 6 decimal places]

Therefore, 12^(-5) * 127 is approximately equal to 0.000508.