Question

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

The product rule of integer exponents states that when multiplying two powers with the same base, you add their exponents. In this case, we have 12^-5 multiplied by 12^7.

To find the numerical value, we can simplify each term separately using the product rule:

12^-5 = 1/(12^5)
12^7 = 12 * 12 * 12 * 12 * 12 * 12 * 12

Now, we can calculate each term separately:

12^7 = 12 * 12 * 12 * 12 * 12 * 12 * 12 = 35,831,808

12^(-5) = 1/(12^5) = 1/(12 * 12 * 12 * 12 * 12) = 1/248,832

Finally, we multiply the two results:

12^(-5) * 12^7 = (1/248,832) * 35,831,808 = 143,165,576/248,832

So, the numerical equivalent of 12^(-5) * 12^7 is 575/1, which can also be written as 575.