Bot GPT 4-o 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:
\[ \boxed{2^{26} \times 3^5} \]
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