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Question
Simplify:
`((9)^3 xx 27 xx t^4)/((3)^-2 xx (3)^4 xx t^2)`
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Solution
Given, `((9)^3 xx 27 xx t^4)/((3)^-2 xx (3)^4 xx t^2)`
= `((3^2)^3 xx (3)^3 xx t^4)/((3)^-2 xx (3)^4 xx t^2)` ...[∵ 3 × 3 = 32 = 9]
= `((3)^6 xx (3)^3 xx t^4)/((3)^-2 xx (3)^4 xx t^2)`
= (3)6 × (3)3 × (3)2 × (3)–4 × t4 × t–2 ...`[∵ a^-m = 1/a^m]`
= (3)11 – 4 × t4 – 2 ...[∵ am × an = (a)m – n]
= (3)7 × t2
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