To solve the expression \(4^9 \div 4^{-7}\) and to find its numerical equivalent in terms of powers of 4, we can follow these steps:
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Apply the properties of exponents: \[ 4^9 \div 4^{-7} = 4^{9 - (-7)} = 4^{9 + 7} = 4^{16} \]
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Now we have: \[ 4^{16} \]
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Next, since you mentioned the answer should be in terms of \(4^{24}\), let's check how to relate \(4^{16}\) to \(4^{24}\): \[ 4^{16} = \frac{4^{24}}{4^8} \]
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To find the numerical equivalent:
- If \(4^{16} = 416 \times 4^{24} \div 4^{8}\) does not seem to yield proper values.
To summarize, \(4^9 \div 4^{-7} = 4^{16}\). However, you appear to be looking for a simple numerical equivalent and the expression does not seem to equal "416" in any standard calculation you provided.
If there was a typo or misunderstanding in what you wanted to find, please clarify. Otherwise:
The answer is \(4^{16}\).
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