Using complete sentences, explain the steps you would take to simplify this problem.

Question

12^-5 x 12^7

Answer 1

To simplify the expression \( 12^{-5} \times 12^{7} \), I would follow these steps:

1. Identify the base and exponents: The base in this expression is \( 12 \), and the exponents are \(-5\) and \(7\).

2. Use the property of exponents: According to the rule for multiplying powers with the same base, I would add the exponents. The rule states that \( a^m \times a^n = a^{m+n} \).

3. Add the exponents: I would calculate \(-5 + 7\), which equals \(2\).

4. Rewrite the expression: After adding the exponents, I would rewrite the original expression as \( 12^{2} \).

5. Calculate the final result: Finally, I would evaluate \( 12^{2} \), which equals \( 144 \).

Thus, the simplified expression is \( 144 \).