Question

Simplify 4 superscript 13 ÷ 3 superscript −5
.(1 point)

Answer 1

To simplify the expression \( 4^{13} \div 3^{-5} \), we can follow these steps:

1. Rewrite the division as multiplication by the reciprocal:
\[
4^{13} \div 3^{-5} = 4^{13} \cdot 3^{5}
\]

2. The expression is now:
\[
4^{13} \cdot 3^{5}
\]

3. This is already in a simplified form. If we wanted to express \( 4^{13} \) in terms of base \( 2 \), we can rewrite \( 4 \) as \( 2^2 \):
\[
4^{13} = (2^2)^{13} = 2^{26}
\]

4. Therefore, the entire expression can be rewritten as:
\[
2^{26} \cdot 3^{5}
\]

So, the simplified expression is:
\[
\boxed{2^{26} \cdot 3^{5}}
\]