Question
Evaluate. Write your answer as a whole number or as a simplified fraction. \[ \frac{4^{9}}{4^{5}}=\square \]
Ask by Conner Luna. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \frac{4^{9}}{4^{5}} = 256 \)
Solution
Calculate or simplify the expression \( \frac{4^{9}}{4^{5}} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{4^{9}}{4^{5}}\)
- step1: Multiply by \(a^{-n}:\)
\(4^{9}\times 4^{-5}\)
- step2: Multiply:
\(4^{9-5}\)
- step3: Subtract the numbers:
\(4^{4}\)
- step4: Evaluate the power:
\(256\)
The value of \( \frac{4^{9}}{4^{5}} \) is 256.
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Simplify this solution The Deep Dive
To evaluate \(\frac{4^{9}}{4^{5}}\), we can use the properties of exponents. According to the quotient rule of exponents, when we divide two powers with the same base, we subtract the exponents. So, we have: \[ \frac{4^{9}}{4^{5}} = 4^{9 - 5} = 4^{4}. \] Now, calculating \(4^{4}\): \[ 4^{4} = 4 \times 4 \times 4 \times 4 = 256. \] Thus, the answer is: \[ \boxed{256}. \]
