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प्रश्न
If `[ 9^n. 3^2 . 3^n - (27)^n]/[ (3^m . 2 )^3 ] = 3^-3`
Show that : m - n = 1.
उत्तर
`[ 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 )
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