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prealgebra intermediate

Problem

When you simplify

[3 6 a^{9}]^{4} [6 3 a^{9}]^{4}

, the result is:

(A)

a^{16}

(B)

a^{12}

(C)

a^{8}

(D)

a^{4}

Solution

This simplifies to

(a^{\frac{9}{6} /3})^{4} \cdot (a^{\frac{9}{3} /6})^{4} = (a^{\frac{1}{2}})^{4} \cdot (a^{\frac{1}{2}})^{4} = (a^{2}) (a^{2}) = a^{4}

The answer is

a^{4} .

Final answer

D