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Question
Simplify the following:
`(5xx25^(n+1)-25xx5^(2n))/(5xx5^(2n+3)-25^(n+1))`
Solution
`(5xx25^(n+1)-25xx5^(2n))/(5xx5^(2n+3)-25^(n+1))`
`=(5xx(5^2)^(n+1)-(5^2)xx5^(2n))/(5xx5^(2n+3)-(5^2)^(n+1))`
`=(5xx(5^(2n+2))-(5^2)xx5^(2n))/(5xx5^(2n+3)-5^(2n+2))`
`=(5^(1+2n+2)-5^(2+2n))/(5^(1+2n+3)-5^(2n+2))`
`=(5^(2+2n)(5-1))/(5^(2+2n)(5^2-1))`
`=(5-1)/(5^2-1)`
`=4/24`
`=1/6`
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