The value of (256)^0.16×(256)^0.09 is:

1959 AMC 12 Problem 5

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The value of

(256)^{0.16}\cdot(256)^{0.09}

is:

4

16

64

256.25

-16

Add the exponents because the bases are equal

The sum of the decimal exponents is

\frac{1}{4}

Using the product rule for powers,

\begin{aligned} 256^{0.16}\cdot256^{0.09} &=256^{0.25}\\ &=256^{\frac{1}{4}}=4. \end{aligned}

Therefore, the correct answer is A.