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Product Law

If 9n× 32× 3-...

Question

If $\frac{9^{n} \times 3^{2} \times (3^{- n / 2})^{- 2} - (27)^{n}}{3^{3 m} \times 2^{3}}$ = $\frac{1}{27}$ , prove that m - n = 1.

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\frac{9^{n} \times 3^{2} \times {(3^{- n / 2})}^{- 2} - {(27)}^{n}}{3^{3 m} \times 2^{3}} = \frac{1}{27}

m - n = 1

.

\frac{9^{n} \times 3^{2} \times {(3}^{- \frac{n}{2}})^{- 2} - 27^{n}}{3^{3 m} \times 2^{3}} = \frac{1}{27}

Prove that m-n=1

\frac{9^{n} \times 3^{2} \times 3^{n} - (27)^{n}}{3^{3 m} \times 2^{3}} = 3^{- 3}

(m - n) = 1

\frac{9^{n} \times 3^{2} \times (3 \frac{n}{2}) - (27)^{n}}{3^{3 m} \times 2^{3}} = \frac{1}{27}

\frac{9^{n + 1} \times {(3 \frac{- n}{2})}^{- 2} - 27^{n}}{{(3^{m} \times 2)}^{3}} = \frac{1}{729}

m - n = 2

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