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Question
Evaluate:
`(15^4 xx 18^3)/(3^3 xx 5^2 xx 12^2)`
Solution
We have, `(15^4 xx 18^3)/(3^3 xx 5^2 xx 12^2) = ((3 xx 5)^4 xx (2 xx 3^2)^3)/(3^3 xx 5^2 xx (2^2 xx 3)^2)` ......[∵ 18 = 2 × 3 × 3 and 12 = 2 × 2 × 3]
= `(3^4 xx 5^4 xx 2^3 xx 3^6)/(3^3 xx 5^2 xx 2^4 xx 3^2)` ......[∵ (a × b)m = am × bm]
= `(3^(4+6-3-2) xx 5^(4-2))/(2^(4-3))` ......`[∵ a^m/a^n = a^(m-n) and a^m xx a^n = a^(m+n)]`
= `(3^5 xx 5^2)/2`
= `(243 xx 25)/2`
= `6075/2`
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