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Question
Evaluate:
`(5^4 xx 7^4 xx 2^7)/(8 xx 49 xx 5^3)`
Solution
We have, `(5^4 xx 7^4 xx 2^7)/(8 xx 49 xx 5^3) = (5^4 xx 7^4 xx 2^7)/(2^3 xx 7^2 xx 5^3)` ......[∵ 8 = 23 and 49 = 72]
= `(5^4/5^3) xx (2^7/2^3) xx (7^4/7^2)` = 54–3 × 27–3 × 74–2 .....`[∵ a^m/a^n = a^(m-n)]`
= 5 × 24 × 72
= 5 × 16 × 49
= 3920
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