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.(2 points)

3 answers

To apply the product rule of integer exponents to find the numerical equivalent of 12^(-5) * 127, we first need to understand the rule.

The product rule of integer exponents states that when multiplying numbers with the same base but different exponents, you can add the exponents and keep the base the same.

In this case, we have 12^(-5) * 127. The base is 12 and the exponents are -5 and 1.

Using the product rule of integer exponents, we add the exponents:

12^(-5) * 127 = 12^(-5+1) * 127

Since -5+1 equals -4, we can rewrite the expression as:

12^(-5) * 127 = 12^(-4) * 127

Now, to find the numerical equivalent, we calculate 12^(-4):

12^(-4) = 1 / 12^4 = 1 / 20736 = 0.000048

Now we can multiply this result by 127:

0.000048 * 127 = 0.006096

Therefore, the numerical equivalent of 12^(-5) * 127 is 0.006096.

By applying the product rule of integer exponents, we were able to simplify the expression and find the numerical value.

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