Question
Simplify to a single power of 4: \[ \left(4^{4}\right)^{5} \]
Ask by Donnelly Smith. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \(4^{20}\).
Solution
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Beyond the Answer
To simplify \(\left(4^{4}\right)^{5}\), we can use the power of a power property of exponents, which states that \((a^{m})^{n} = a^{m \cdot n}\). Applying this property here, we have: \[ \left(4^{4}\right)^{5} = 4^{4 \cdot 5} \] Calculating the exponent: \[ 4 \cdot 5 = 20 \] Thus, we find: \[ \left(4^{4}\right)^{5} = 4^{20} \] So, the simplified expression is: \[ 4^{20} \]
