Question
Using complete sentences, explain the steps you would take to simplify this problem.
12^-5 x 12^7
12^-5 x 12^7
Answers
GPT-4o mini
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 \( 144 \).
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 \( 144 \).