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prealgebra intermediate

Problem

4^{4} \cdot 9^{4} \cdot 4^{9} \cdot 9^{9} =

(A)

1 3^{1} 3

(B)

1 3^{3} 6

(C)

3 6^{1} 3

(D)

3 6^{3} 6

Solution

Note that

a^{x} \times a^{y} = a^{x + y}

. So

4^{4} \cdot 4^{9} = 4^{13}

and

9^{4} \cdot 9^{9} = 9^{13}

. Therefore,

4^{13} \cdot 9^{13} = (4 \cdot 9)^{13} = 3 6^{13}

.

Final answer

C