If 9n- 32-3 n-2-27 n -33 m - 23-1-27 then m -A- n -1B- n2-1C- n-1 D- m 2-1- m 2

The correct option is C n + 19^n × 3^2 × (3 n/2)^ 2 (27)^n/3^3m× 2^3= 1/27 ⇒(3^n)^n × 3^2 × 3^n (3^3)^n/3^3m× 2^3 = 1/27 ⇒3^2n + 2 + n3^3n/3^3m × 3 = 1/2 ...

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Byju's Answer

Standard IX

Mathematics

Zero Exponent

If 9n× 32×3 n...

Question

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

n - 1

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n^{2} - 1

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n + 1

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\frac{m^{2} + 1}{m^{2}}

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Solution

The correct option is C $n + 1$
$\frac{9^{n} \times 3^{2} \times (3 - \frac{n}{2})^{- 2} - (27)^{n}}{3^{3 m} \times 2^{3}} = \frac{1}{27} \Rightarrow \frac{(3^{n})^{n} \times 3^{2} \times 3^{n} - (3^{3})^{n}}{3^{3 m} \times 2^{3}} = \frac{1}{27} \Rightarrow \frac{3^{2 n + 2 + n} 3^{3 n}}{3^{3 m \times 3}} = \frac{1}{27} \Rightarrow \frac{3^{3 n} (3^{2} - 1)}{3^{3 m} 8} = \frac{1}{27} \Rightarrow \frac{3^{3 n} \times 8}{3^{3 n} \times 8} = \frac{1}{27} \Rightarrow \frac{3^{3 n}}{3^{3 m}} = \frac{1}{27} = (\frac{1}{3})^{3} \Rightarrow 3^{3 n - 3 m} = 3^{- 3} . \Rightarrow 3 n - 3 m = - 3 \Rightarrow n - m = - 1 \Rightarrow m = 1 + n$

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Similar questions

Q. If

\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

Q. 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

Q. 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.

Q. If

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

, prove that

(m - n) = 1

Q. Solve:

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

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If 9n×32×(3n2)−(27)n33m×23=127 then m =

The correct option is C n+19n×32×(3−n2)−2−(27)n33m×23=127⇒(3n)n×32×3n−(33)n33m×23=127⇒32n+2+n33n33m×3=127⇒33n(32−1)33m8=127⇒33n×833n×8=127⇒33n33m=127=(13)3⇒33n−3m=3−3.⇒3n−3m=−3⇒n−m=−1⇒m=1+n

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