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1. (256)^0.16 × (256)^0.09 = ?

A. 4

B. 16

C. 64

D. 256.25

Solution:

(256)^0.16 × (256)^0.09 = (256)^{(0.16 + 0.09)}

\begin{aligned} = {(256)}^{0.25} \\ = {(256)}^{\frac{25}{100}} \\ = {(256)}^{\frac{1}{4}} \\ = {(4^{4})}^{\frac{1}{4}} \\ = 4^{1} \\ = 4 \end{aligned}

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