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
11801122=1158





6−129−15=915612





(163)9= 1627

Answer 1

Let's look at each expression and apply the relevant exponent rules to simplify them. Here's the completed table with explanations for each rule used:

| Expression | Simplified Form | Exponent Rule Used |
|--------------------------|----------------------|-------------------------------------------------------|
| \(11801122=1158\) | \(1158\) | Product Rule (adding exponents) |
| \(6^{-12}9^{-15} = 9^{15}6^{12}\) | \(9^{15}6^{12}\) | Negative Integer Exponent Rule (moving to the numerator) |
| \((163)^{9} = 162^{7}\) | \(162^{7}\) | Power Rule (multiplying exponents) |

### Explanation of Exponent Rules:

1. **Product Rule**: When multiplying the same base, add the exponents: \(a^m \cdot a^n = a^{m+n}\).

2. **Quotient Rule**: When dividing the same base, subtract the exponents: \(a^m / a^n = a^{m-n}\).

3. **Power Rule**: When raising a power to another power, multiply the exponents: \((a^m)^n = a^{m \cdot n}\).

4. **Negative Integer Exponent Rule**: A negative exponent indicates a reciprocal: \(a^{-n} = 1/a^n\).

5. **Zero Power Rule**: Any non-zero number raised to the power of zero equals one: \(a^0 = 1\).

### Note:
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