Question

Complete the table. For each of the expressions, choose which exponent rule has been used to simplify.(3 points)Product Rule Quotient Rule Power Rule Negative Integer Exponent Rule Zero Power Rule

(16^3)^9= 16^27
11^80/11^22=11^58
6^-12/9^−15=9^15/6^12

Answer 1

Here's the completed table with the appropriate exponent rules for each expression:

| Expression | Exponent Rule |
|--------------------------------------|-----------------------------------------|
| \((16^3)^9 = 16^{27}\) | Power Rule |
| \(\frac{11^{80}}{11^{22}} = 11^{58}\)| Quotient Rule |
| \(\frac{6^{-12}}{9^{-15}} = \frac{9^{15}}{6^{12}}\)| Negative Integer Exponent Rule |

### Explanation:
1. **Power Rule** states that \((a^m)^n = a^{m \cdot n}\).
2. **Quotient Rule** states that \(\frac{a^m}{a^n} = a^{m-n}\).
3. **Negative Integer Exponent Rule** states that \(a^{-m} = \frac{1}{a^m}\) and can also be applied to help convert the expression to a more simplified form.

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