Question

Develop the Negative Power Rule for exponents to continue the pattern:

6 2=36

6 1=6

6 0=1

6 −1=16

6 −2=?

(1 point)
Responses

6 −2=36
6 superscript negative 2 baseline equals 36

6 −2=1/36
6 superscript negative 2 baseline equals Start Fraction 1 over 36 End Fraction

6 −2=1
6 superscript negative 2 baseline equals 1

6 −2=1/12

Answer 1

To develop the Negative Power Rule for exponents and continue the pattern, we can observe the following:

1. **Exponents of 2, 1, 0, -1:**
- \(6^2 = 36\)
- \(6^1 = 6\)
- \(6^0 = 1\)
- \(6^{-1} = \frac{1}{6}\)

2. **Working with negative exponents:**
- From the negative exponent rule, \(a^{-n} = \frac{1}{a^n}\), we deduce that:
- \(6^{-1} = \frac{1}{6^1} = \frac{1}{6}\)

3. **For \(6^{-2}\):**
- According to the negative exponent rule, \(6^{-2} = \frac{1}{6^2} = \frac{1}{36}\).

Thus, the correct answer is:

\[6^{-2} = \frac{1}{36}\]

So the response to select is:

**6 −2=1/36**