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Simplify the Following: `(6(8)^(N+1)+16(2)^(3n-2))/(10(2)^(3n+1)-7(8)^N)` - CBSE Class 9 - Mathematics

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Question

Simplify the following:

`(6(8)^(n+1)+16(2)^(3n-2))/(10(2)^(3n+1)-7(8)^n)`

Solution

`(6(8)^(n+1)+16(2)^(3n-2))/(10(2)^(3n+1)-7(8)^n)`

`=(6(2^3)^(n+1)+16(2)^(3n-2))/(10(2)^(3n+1)-7(2^3)^n)`

`=(6(2^(3n+3))+16(2)^(3n-2))/(10(2)^(3n+1)-7(2^(3n)))`

`=(6xx2^(3n)(2^3)+16(2)^(3n)2^-2)/(10(2)^(3n)(2^1)-7(2^(3n)))`

`=(2^(3n)((6xx2^3)+(16xx1/2^2)))/(2^(3n)((10xx2)-7))`

`=((6xx8)+(16xx1/4))/(20-7)`

`=(48+4)/(13)`

`=52/13`

= 4

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 2: Exponents of Real Numbers
Ex. 2.10 | Q: 7.4 | Page no. 12

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Solution Simplify the Following: `(6(8)^(N+1)+16(2)^(3n-2))/(10(2)^(3n+1)-7(8)^N)` Concept: Laws of Exponents for Real Numbers.
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