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Simplify \(\frac{6^{2n + 1} \times 9^n \times 4^{2n}}{18^n \...

Simplify $\frac{6^{2n + 1} \times 9^n \times 4^{2n}}{18^n \times 2^n \times 12^{2n}}$

A.

3²ⁿ

B.

3 x 2^{3n - 1}

C.

2ⁿ

D.

6

E.

1

View answer & explanation

Correct answer is D

$\frac{6^{2n + 1} \times 9^n \times 4^{2n}}{18^n \times 2^n \times 12^{2n}}$ = $\frac{(2 \times 3^{2n + 1} \times 3^{2n}) \times 2^{4n}}{(2 \times 9)^n \times 2^n \times (6 \times 2^{2n})}$

= $\frac{(2^{2n + 1} \times 3^{2n + 1}) \times 3^{2n} \times 2^{4n}}{2^n \times 3^{2n} \times 2^n \times 2^{4n} \times 3^{2n}}$

= $\frac{2^{2n} + 1 + 4^n \times 3^{2n} + 1 + 2^n}{2^{n + n + 4n} \times 3^{2n + 4n} \times 3^{2n + 2n}}$

= $\frac{2^{6n + 1} \times 3^{4n + 1}}{2^{6n} x 3^{4n}}$

= 2^{6n + 1 - 6n} x 3^{4n + 1 - 4n}

2 x 3 = 6

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