QuestionJuly 18, 2025

9. 4^-5div 4^-8=underline ( )=underline ( )

9. 4^-5div 4^-8=underline ( )=underline ( )
9. 4^-5div 4^-8=underline ( )=underline ( )

Solution
4.3(217 votes)

Answer

4^3 = 64 Explanation 1. Apply the Division Rule for Exponents Use the rule **a^m \div a^n = a^{m-n}**. Here, m = -5 and n = -8. 2. Simplify the Exponent Calculate -5 - (-8) = -5 + 8 = 3. So, 4^{-5} \div 4^{-8} = 4^3. 3. Calculate the Power Compute 4^3 = 4 \times 4 \times 4 = 64.

Explanation

1. Apply the Division Rule for Exponents<br /> Use the rule **$a^m \div a^n = a^{m-n}$**. Here, $m = -5$ and $n = -8$.<br />2. Simplify the Exponent<br /> Calculate $-5 - (-8) = -5 + 8 = 3$. So, $4^{-5} \div 4^{-8} = 4^3$.<br />3. Calculate the Power<br /> Compute $4^3 = 4 \times 4 \times 4 = 64$.
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