Question
Apply the product rule of exponents to find the numerical equivalent of 12^-5 x 12^7. Show your work and explain how you used the product rule of integer exponents
Answers
GPT 3.5
The product rule of exponents states that when multiplying two numbers with the same base, you add the exponents. In other words, a^m * a^n = a^(m+n).
In this case, we have 12^-5 * 12^7. Since the base, 12, is the same, we can apply the product rule of exponents.
First, we add the exponents: (-5) + 7 = 2.
So, 12^-5 * 12^7 can be simplified to 12^2.
To find the numerical equivalent of 12^2, we simply calculate 12^2 as follows:
12^2 = 12 * 12 = 144.
Therefore, the numerical equivalent of 12^-5 * 12^7 is 144.
In this case, we have 12^-5 * 12^7. Since the base, 12, is the same, we can apply the product rule of exponents.
First, we add the exponents: (-5) + 7 = 2.
So, 12^-5 * 12^7 can be simplified to 12^2.
To find the numerical equivalent of 12^2, we simply calculate 12^2 as follows:
12^2 = 12 * 12 = 144.
Therefore, the numerical equivalent of 12^-5 * 12^7 is 144.