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Question
Simplify:
`((3^-2)^2 xx (5^2)^-3 xx (t^-3)^2)/((3^-2)^5 xx (5^3)^-2 xx (t^-4)^3`
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Solution
Given, `((3^-2)^2 xx (5^2)^-3 xx (t^-3)^2)/((3^-2)^5 xx (5^3)^-2 xx (t^-4)^3`
= `((3)^-4 xx (5)^-6 xx (t)^-6)/((3)^-10 xx (5)^-6 xx (t)^-12)` ...[∵ a–m × (a)mn]
= `(3)^-4 × (3)^10 × (5)^-6 × (5)^6 × (t)^-6 × (t)^12`
= `(3)^(-4 + 10) xx (5)^(-6 + 5) xx (t)^(-6 + 12)` ...`[∵ a^-m = 1/a^m]`
= (3)6 × 50 × (t)6 ...[∵ a0 = 1]
= (3t)6
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