Question
Develop the Negative Power Rule for exponents to continue the pattern: 62=36 61=6 60=1 6−1=16 6−2=? (1 point) Responses 6−2=36 6 superscript negative 2 baseline equals 36 6−2=112 6 superscript negative 2 baseline equals Start Fraction 1 over 12 End Fraction 6−2=1 6 superscript negative 2 baseline equals 1 6−2=136 6 superscript negative 2 baseline equals Start Fraction 1 over 36 End Fraction Skip to navigation
Answers
Answered by
GPT-4o mini
To develop the Negative Power Rule for exponents, we can follow the pattern established by the previous equations.
Given:
- \( 6^2 = 36 \)
- \( 6^1 = 6 \)
- \( 6^0 = 1 \)
- \( 6^{-1} = \frac{1}{6} \)
The negative exponent rule states that \( a^{-n} = \frac{1}{a^n} \). Thus, for \( 6^{-2} \):
\[
6^{-2} = \frac{1}{6^2}
\]
From \( 6^2 = 36 \), we substitute this value in:
\[
6^{-2} = \frac{1}{36}
\]
Therefore, the correct completion of the pattern is:
\[
6^{-2} = \frac{1}{36}
\]
So the answer is:
\( 6^{-2} = \frac{1}{36} \)
Given:
- \( 6^2 = 36 \)
- \( 6^1 = 6 \)
- \( 6^0 = 1 \)
- \( 6^{-1} = \frac{1}{6} \)
The negative exponent rule states that \( a^{-n} = \frac{1}{a^n} \). Thus, for \( 6^{-2} \):
\[
6^{-2} = \frac{1}{6^2}
\]
From \( 6^2 = 36 \), we substitute this value in:
\[
6^{-2} = \frac{1}{36}
\]
Therefore, the correct completion of the pattern is:
\[
6^{-2} = \frac{1}{36}
\]
So the answer is:
\( 6^{-2} = \frac{1}{36} \)