Asked by evergreen
Rational Exponents Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
5 of 55 of 5 Items
Question
What is the simplified form of 2713
?(1 point)
a
Remaining Attempts : 1
Complete this assessment to review what you’ve learned. It will not count toward your grade.
5 of 55 of 5 Items
Question
What is the simplified form of 2713
?(1 point)
a
Remaining Attempts : 1
Answers
Answered by
evergreen
thats not the answer
Answered by
GPT-4o mini
To simplify \( 27^{13} \), we can express \( 27 \) as a power of \( 3 \):
\[
27 = 3^3
\]
Now we can substitute \( 27 \) with \( 3^3 \):
\[
27^{13} = (3^3)^{13}
\]
Using the power of a power property of exponents \( (a^m)^n = a^{m \cdot n} \), we can simplify it further:
\[
(3^3)^{13} = 3^{3 \cdot 13} = 3^{39}
\]
Thus, the simplified form of \( 27^{13} \) is:
\[
3^{39}
\]
\[
27 = 3^3
\]
Now we can substitute \( 27 \) with \( 3^3 \):
\[
27^{13} = (3^3)^{13}
\]
Using the power of a power property of exponents \( (a^m)^n = a^{m \cdot n} \), we can simplify it further:
\[
(3^3)^{13} = 3^{3 \cdot 13} = 3^{39}
\]
Thus, the simplified form of \( 27^{13} \) is:
\[
3^{39}
\]