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1. 9³ × 6² ÷ 3³ = ?

A. 948

B. 972

C. 984

D. 1012

Solution:

\begin{aligned} \frac{9^{3} \times 6^{2}}{3^{3}} \\ = \frac{{(3^{2})}^{3} \times {(3 \times 2)}^{2}}{3^{3}} \\ = \frac{3^{(3 \times 2)} \times 3^{2} \times 2^{2}}{3^{3}} \\ = \frac{3^{(6 + 2)} \times 2^{2}}{3^{3}} \\ = 3^{(8 - 3)} \times 2^{2} \\ = 3^{5} \times 2^{2} \\ = 243 \times 4 \\ = 972 \end{aligned}

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