# Simplify : 3 Xx 27^( N + 1 ) + 9 Xx 3^(3n - 1 )/ 8 Xx 3^(3n) - 5 Xx 27^N - Mathematics

Sum

Simplify :
[ 3 xx 27^( n + 1 ) + 9 xx 3^(3n - 1 )]/[ 8 xx 3^(3n) - 5 xx 27^n ]

#### Solution

[ 3 xx 27^( n + 1 ) + 9 xx 3^(3n - 1 )]/[ 8 xx 3^(3n) - 5 xx 27^n ]

= [ 3 xx ( 3 xx 3 xx 3 )^( n + 1 ) + 3 xx 3 xx 3^(3n - 1 )]/[2 xx 2 xx 2 xx 3^(3n) - 5 xx ( 3 xx 3 xx 3)^n]

= [ 3 xx (3^3)^(n + 1) + 3^2 xx 3^(3n - 1 )]/[ 2^3 xx 3^(3n) - 5 xx (3^3)^n]

= [ 3 xx 3^( 3n + 3 ) + 3^( 3n + 1 )]/[2^3 xx (3^3)^n - 5 xx (3^3)^n ]

= [ 3^(3n + 3 + 1) + 3^(3n + 1)]/[ 2^3 xx (3^3)^n - 5 xx (3^3)^n ]

= [ 3^(3n + 4) + 3^(3n + 1)]/[2^3 xx (3^3)^n - 5 xx (3^3)^n ]

= [ 3^(3n) xx 3^4 + 3^(3n) xx 3^1 ]/[2^3 xx (3^3)^n - 5 xx (3^3)^n ]

= [ 3^(3n)( 3^4 + 3^1 )]/[(3^3)^n ( 8 - 5 )]

= [ 3^(3n)( 3^4 + 3^1 )]/[ 3^(3n) xx 3]

= [ 3 xx 3 xx 3 xx 3 + 3]/3

= [ 81 + 3 ]/3

= 84/3

= 28

Concept: Laws of Exponents
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#### APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (A) | Q 7.2 | Page 98