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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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