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
.
13⋅13⋅13⋅13\frac{1}{3}\cdot\frac{1}{3}\cdot\frac{1}{3}\cdot\frac{1}{3}
3
1
⋅
3
1
⋅
3
1
⋅
3
1
5
3
1
not 5−35^{-3}5
−3
.
13⋅13⋅13⋅13\frac{1}{3}\cdot\frac{1}{3}\cdot\frac{1}{3}\cdot\frac{1}{3}
3
1
⋅
3
1
⋅
3
1
⋅
3
1
Answers
GPT-4o mini
To simplify the expression \( 13 \cdot 13 \cdot 13 \cdot 13 \cdot \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} \), we first group the terms.
1. The first part \( 13 \cdot 13 \cdot 13 \cdot 13 \) can be rewritten using exponents:
\[
13^4
\]
2. The second part \( \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} \) can also be rewritten using exponents:
\[
\left(\frac{1}{3}\right)^4 = \frac{1^4}{3^4} = \frac{1}{3^4}
\]
3. Combining these two simplified parts:
\[
13^4 \cdot \frac{1}{3^4} = \frac{13^4}{3^4}
\]
4. Finally, this can be expressed in exponential form:
\[
\left(\frac{13}{3}\right)^4
\]
Thus, the fully simplified result is:
\[
\left(\frac{13}{3}\right)^4
\]
1. The first part \( 13 \cdot 13 \cdot 13 \cdot 13 \) can be rewritten using exponents:
\[
13^4
\]
2. The second part \( \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} \) can also be rewritten using exponents:
\[
\left(\frac{1}{3}\right)^4 = \frac{1^4}{3^4} = \frac{1}{3^4}
\]
3. Combining these two simplified parts:
\[
13^4 \cdot \frac{1}{3^4} = \frac{13^4}{3^4}
\]
4. Finally, this can be expressed in exponential form:
\[
\left(\frac{13}{3}\right)^4
\]
Thus, the fully simplified result is:
\[
\left(\frac{13}{3}\right)^4
\]