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)

Answer 1

To use the product rule of integer exponents, we need to apply it to each term separately.

Starting with the first term, 12^(-5), we can rewrite it as 1/(12^5). This is because a negative exponent means to take the reciprocal of the base raised to the positive exponent.

Next, we have 127. We can rewrite it as 127^1.

Now, we can use the product rule of integer exponents, which states that when multiplying two terms with the same base raised to different exponents, we can simply add the exponents.

So, 12^(-5) * 127^1 becomes 1/(12^5) * 127^1.

Applying the product rule, we add the exponents: 1/(12^5 * 127^1).

Now, we can simplify the expression by evaluating the base raised to the exponents. 12^5 = 248,832 and 127^1 = 127.

Therefore, the numerical equivalent of 12^(-5) * 127^1 is 1/(248,832 * 127) = 1/31,604,064.