Find the value of m - n, if ( 9n x 32 x (3-n/2)-2

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Find the value of m - n, if ( 9n x 32 x (3-n/2)-2 - (27)n

Home » Aptitude » Surds and Indices » Question

Find the value of m - n, if ( 9ⁿ x 3² x (3^-n/2)^-2 - (27)ⁿ ) / ( 3^3m x 2³ ) = 1/27 ?

1. 1
2. -2
3. -1
4. 2

Correct Option: A

( 9ⁿ x 3² x (3^-n/2)^-2 - (27)ⁿ ) / ( 3^3m x 2³ ) = 1/27
⇒ ( 3²ⁿ x 3² x 3ⁿ - 3³ⁿ) / ( 3^3m x 2³ ) = 1/27
⇒ ( 3^{2n + n} x 3² - 3³ⁿ) / ( 3^3m x 2³ )= 1/27
⇒ ( 3³ⁿ x 3² - 3³ⁿ) / ( 3^3m x 2³ ) = 1/27
⇒ 3³ⁿ( 3² - 1) / ( 3^3m x 8 ) = 1/27
⇒ 3³ⁿ( 9 - 1) / (3^3m x 8 ) = 1/27
⇒ ( 3³ⁿ x 8 ) / (3^3m x 8 ) = 1/27
⇒ 3³ⁿ / 3^3m = 1/27
⇒ 3^{3n - 3m} = 1/3³
⇒ 3³^{( n - m )} = 3^-3
3(n - m) = -3
or n - m = -1
or m - n = 1