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Question
Evaluate:
`(6^4 xx 9^2 xx 25^3)/(3^2 xx 4^2 xx 15^6)`
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Solution
We have, `(6^4 xx 9^2 xx 25^3)/(3^2 xx 4^2 xx 15^6) = ((2 xx 3)^4 xx (3^2)^2 xx (5^2)^3)/(3^2 xx (2^2)^2 xx (3 xx 5)^6)`
= `(2^4 xx 3^4 xx 3^4 xx 5^6)/(3^2 xx 2^4 xx 3^6 xx 5^6)` ...[∵ (a × b)m = am × bm]
= `2^(4 - 4) xx 3^(4 + 4 - 2 - 6) xx 5^(6 - 6)` ...`[∵ a^m/a^n = a^(m - n)]`
= 20 × 30 × 50
= 1 × 1 × 1
= 1
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