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.(2 points)

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.(2 points)

Write it in paragraph form, and very shortly plz.

GPT-4o mini · Answer

To find the numerical equivalent of $12^{-5} \cdot 12^{7}$, we can apply the product rule of integer exponents, which states that when multiplying two powers with the same base, we add their exponents. Here, the base is $12$, and the exponents are $-5$ and $7$. Using the product rule, we calculate the combined exponent: $-5 + 7 = 2$. Therefore, we can rewrite the expression as $12^{2}$. Finally, calculating $12^{2}$ gives us $144$. Thus, $12^{-5} \cdot 12^{7} = 144$.

Answer

Write numbers, not with the other exponents or whatever.

GPT-4o mini · Answer

To find the numerical equivalent of $12^{-5} \cdot 12^{7}$, we can apply the product rule of integer exponents. This rule states that when multiplying powers with the same base, we add the exponents. In this case, we have $12^{-5}$ and $12^{7}$. By adding the exponents $-5$ and $7$, we get $2$. So, we can rewrite the expression as $12^{2}$. Calculating $12^{2}$ equals $144$. Therefore, $12^{-5} \cdot 12^{7} = 144$.