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If 9^N. 3^2 . 3^N - (27)^N/(3^M . 2 )^3 = 3^-3 Show that : M - N = 1. - Mathematics

Sum

If `[ 9^n. 3^2 . 3^n - (27)^n]/[ (3^m . 2 )^3 ] = 3^-3`

Show that : m - n = 1.

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Solution

`[ 9^n. 3^2 . 3^n - (27)^n]/[ (3^m . 2 )^3 ] = 3^-3`

⇒ `[ 3^(2n). 3^2 . 3^n - (3)^(3n)]/[3^(3m) . (2)^3]  = 1/3^3`

⇒ `[ 3^(3n) . 3^2 - 3^(3n) ]/[ 3^(3m) . 2^3 ] = 1/3^3`

⇒ `[ 3^(3n)( 3^2 - 1 ) ]/[ 3^(3m) xx 8 ] = 1/3^3`

⇒ `[ 3^(3n) xx 8 ]/[ 3^(3m) xx 8 ] = 1/3^3`

⇒ `1/[ 3^(3( m - n ))] = 1/3^( 3 xx 1 )`

⇒ m - n = 1  ( proved )

Concept: Simplification of Expressions
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (C) | Q 7 | Page 101
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