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fully simplify and write your answer in exponential form with positive exponents only. example : 1/5 3 not 5 little - 3. 13 little - 6 ÷ 13 ÷ 14 little -2 =
Answers
Answered by
GPT-4o mini
To simplify the expression \( 13^{-6} \div 13 \div 14^{-2} \), we follow these steps:
1. **Rewrite the division as multiplication by the reciprocal:**
\[
13^{-6} \div 13 = 13^{-6} \times 13^{-1}
\]
This simplifies to:
\[
13^{-6 - 1} = 13^{-7}
\]
2. **Now, rewrite the division by \( 14^{-2} \) as multiplication:**
\[
13^{-7} \div 14^{-2} = 13^{-7} \times 14^{2}
\]
3. **Combine the expression:**
\[
13^{-7} \times 14^{2} = \frac{14^{2}}{13^{7}}
\]
4. **Finally, we present the answer in exponential form with positive exponents:**
\[
\frac{14^2}{13^7}
\]
Thus, the simplified expression is:
\[
\frac{14^{2}}{13^{7}}
\]
1. **Rewrite the division as multiplication by the reciprocal:**
\[
13^{-6} \div 13 = 13^{-6} \times 13^{-1}
\]
This simplifies to:
\[
13^{-6 - 1} = 13^{-7}
\]
2. **Now, rewrite the division by \( 14^{-2} \) as multiplication:**
\[
13^{-7} \div 14^{-2} = 13^{-7} \times 14^{2}
\]
3. **Combine the expression:**
\[
13^{-7} \times 14^{2} = \frac{14^{2}}{13^{7}}
\]
4. **Finally, we present the answer in exponential form with positive exponents:**
\[
\frac{14^2}{13^7}
\]
Thus, the simplified expression is:
\[
\frac{14^{2}}{13^{7}}
\]