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Question
Evaluate the following:
`(12^2 xx 75^-2 xx 35 xx 400)/(48^2 xx 15^-3 xx 525)`
Solution
`(12^2 xx 75^-2 xx 35 xx 400)/(48^2 xx 15^-3 xx 525)`
= `((2^2 xx 3)^2 xx (7 xx 5) xx (2^4 xx 5^2) xx (3 xx 5)^3)/((2^4 xx 3^2) xx (3 xx 5^2 xx 7) xx (3 xx 5^2)^2)`
= `(2^4 xx 3^2 xx 7 xx 5 xx 2^4 xx 5^2 xx 3^3 xx 5^3)/(2^8 xx 3^2 xx 3 xx 5^2 xx 7 xx 3^2 xx 5^4)`
= `(2^(4 + 4) xx 3^(2 + 3) xx 5^(1 + 2 + 3) xx 7)/(2^8 xx 3^(2 + 1 + 2) xx 5^(4 + 2) xx 7)`
= `(2^8 xx 3^5 xx 5^6 xx 7)/(2^8 xx 3^5 xx 5^6 xx 7)`
= 1.
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