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Question
Evaluate:
`(125 xx 5^2 xx a^7)/(10^3 xx a^4)`
Solution
We have, `(125 xx 5^2 xx a^7)/(10^3 xx a^4) = (5^3 xx 5^2 xx a^7)/((2 xx 5)^3 xx a^4)` ......[∵ 125 = 53]
= `(5^(3+2) xx a^7)/(2^3 xx 5^3 xx a^4)` ......[∵ am × an = am+n and (a × b)m = am × bm]
= `(5^5 xx a^7)/(2^3 xx 5^3 xx a^4)`
= `(5^5/5^3) xx (a^7/a^4) xx (1/2^3)`
= `(5^(5-3) xx a^(7-4))/2^3` ......`[∵ a^m/a^n = a^(m-n)]`
= `(5^2 xx a^3)/2^3`
= `(25a^3)/8`
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