Advertisement Remove all ads

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 ]`

Advertisement Remove all ads

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
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (A) | Q 7.2 | Page 98
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×