Question
Fully simplify and write your answer in exponential form with positive exponents only. Example: 153\frac{1}{5^3}
5
3
1
not 5−35^{-3}5
−3
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11−8⋅11⋅11−6=11^{-8}\cdot11\cdot11^{-6}=11
−8
⋅11⋅11
−6
=
Answers
Answered by
GPT-4o mini
To simplify the expression \( 11^{-8} \cdot 11 \cdot 11^{-6} \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).
Let's break it down step by step:
1. Rewrite the expression:
\[
11^{-8} \cdot 11^1 \cdot 11^{-6}
\]
2. Now, add the exponents:
\[
-8 + 1 - 6
\]
3. Calculate the sum:
\[
-8 + 1 = -7
\]
\[
-7 - 6 = -13
\]
Thus, we have:
\[
11^{-13}
\]
4. To express this in positive exponent form, we use the property \( a^{-m} = \frac{1}{a^m} \):
\[
11^{-13} = \frac{1}{11^{13}}
\]
Therefore, the fully simplified expression is:
\[
\frac{1}{11^{13}}
\]
Let's break it down step by step:
1. Rewrite the expression:
\[
11^{-8} \cdot 11^1 \cdot 11^{-6}
\]
2. Now, add the exponents:
\[
-8 + 1 - 6
\]
3. Calculate the sum:
\[
-8 + 1 = -7
\]
\[
-7 - 6 = -13
\]
Thus, we have:
\[
11^{-13}
\]
4. To express this in positive exponent form, we use the property \( a^{-m} = \frac{1}{a^m} \):
\[
11^{-13} = \frac{1}{11^{13}}
\]
Therefore, the fully simplified expression is:
\[
\frac{1}{11^{13}}
\]