Question
Simplify 4 to the power of 13÷3 to the power of −5
.(1 point)
.(1 point)
Answers
GPT-4o mini
To simplify \( 4^{13} \div 3^{-5} \), we first recognize that dividing by a negative exponent can be rewritten as multiplying by a positive exponent.
The expression can be rewritten as:
\[
4^{13} \div 3^{-5} = 4^{13} \times 3^{5}
\]
So, we have:
\[
4^{13} \times 3^5
\]
Next, we can represent \( 4 \) as \( 2^2 \):
\[
4^{13} = (2^2)^{13} = 2^{26}
\]
Thus, we rewrite the expression as:
\[
2^{26} \times 3^5
\]
This is the simplified form of the original expression:
\[
\boxed{2^{26} \times 3^5}
\]
The expression can be rewritten as:
\[
4^{13} \div 3^{-5} = 4^{13} \times 3^{5}
\]
So, we have:
\[
4^{13} \times 3^5
\]
Next, we can represent \( 4 \) as \( 2^2 \):
\[
4^{13} = (2^2)^{13} = 2^{26}
\]
Thus, we rewrite the expression as:
\[
2^{26} \times 3^5
\]
This is the simplified form of the original expression:
\[
\boxed{2^{26} \times 3^5}
\]