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Question
Simplify.
`(25 xx t^(-4))/(5^(-3) xx10xxt^(-8)) (t != 0)`
Solution
We have,
`(25 xx t^(-4))/(5^(-3) xx10xxt^(-8))`
`= ((5) xx t^-4)/ ((5)^-3 xx (5)^1 xx (2)^1 xx t^-8)`
`= ((5)^2 xx t^-4)/ (5^(-3 +1) xx (2)^1xxt^-8)` ...[∵ am . an = am+n]
`= ((5)^2 xx t^-4)/ ((5)^-2 xx (2)^1 xx t^-8)`
`= ((5)^(2+2) xxt^(-4+8))/ 2` ...`[a^m/a^n = a^(m-n)]`
`= ((5)^4 xxt^4)/2`
`= (625 xxt^4)/2`
`= (625t^4)/2`
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