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Question
Find the value of n, when:
`("a"^(2"n"-3)xx("a"^2)^("n"+1))/(("a"^4)^-3)=("a"^3)^3÷("a"^6)^-3`
Solution
`("a"^(2"n"-3)xx("a"^2)^("n"+1))/(("a"^4)^-3)=("a"^3)^3÷("a"^6)^-3`
`("a"^(2"n"-3)xxa^(2"n"+2))/"a"^-12="a"^9÷"a"^-18`
`("a"^(2"n"-3)xx2^(2"n"+2))/"a"^-12="a"^9/"a"^-18`
`"a"^(2"n"-3+2"n"+2-(-12)="a"^9-(-18))`
`"a"^(4"n"+11)="a"^27`
Comparing both sides, we get
`4"n"+11=27`
`⇒4"n"=27-11`
`⇒"n"=16/4=4`
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