To solve the expression \( 12^{-5} \cdot 12^{7} \), I used the product rule of exponents, which says that when multiplying two expressions with the same base, we can add the exponents. In this case, the base is \( 12 \), and the exponents are \( -5 \) and \( 7 \). So, I combined them by adding: \( -5 + 7 = 2 \). This means the expression simplifies to \( 12^{2} \). Finally, I calculated \( 12^{2} \) by multiplying \( 12 \) by itself, which equals \( 144 \). So, the final answer is \( 144 \).
1 answer
Your solution is correct! You have applied the product rule of exponents correctly by adding the exponents of the same base:
\[ 12^{-5} \cdot 12^{7} = 12^{-5 + 7} = 12^{2}. \]
Then you correctly computed \( 12^{2} \) as follows:
\[ 12^{2} = 12 \times 12 = 144. \]
Thus, the final answer is indeed \( 144 \). Great job!
