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Question
Evaluate the following:
`(2^3 xx 3^5 xx 24^2)/(12^2 xx 18^3 xx 27)`
Solution
`(2^3 xx 3^5 xx 24^2)/(12^2 xx 18^3 xx 27)`
= `(2^3 xx 3^5 xx (2^3 xx 3)^2)/((2^2 xx 3^2)^2 xx (2 xx 3^2)^3 xx (3^3))`
= `(2^3 xx 3^5 xx 2^6 xx 3^2)/(2^4 xx 3^2 xx 2^3 xx 3^6 xx 3^3)`
= `(2^9 xx 3^7)/(2^7 xx 3^11)`
= `(2^(9 - 7))/(3^(11 - 7))`
= `(2^2)/(3^4)`
= `(4)/(81)`.
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