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1. The value of ${(256)}^{\frac{5}{4}}$ is = ?

A. 512

B. 984

C. 1024

D. 1032

Solution:

\begin{aligned} {(256)}^{\frac{5}{4}} \\ = {(4^{4})}^{\frac{5}{4}} \\ = 4^{(4 \times \frac{5}{4})} \\ = 4^{5} \\ = 1024 \end{aligned}

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