Question

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

6^−12/9^−15 =9^15/6^12

(16^3)^9= 16^27

11^80/11^22=11^58

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Answer 1

Here's the completed table with the appropriate exponent rules used to simplify each expression:

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

Explanation of Each Rule:

1. Negative Integer Exponent Rule: This rule states that \( a^{-n} = \frac{1}{a^n} \). In the first expression, the negative exponents are inverted.

2. Power Rule: This rule states that \( (a^m)^n = a^{m \cdot n} \). In the second expression, the powers are multiplied.

3. Quotient Rule: This rule states that \( \frac{a^m}{a^n} = a^{m-n} \). In the third expression, the powers are subtracted.

If you have any further questions or need additional explanations, feel free to ask!