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Question
Evaluate:
`((6 xx 10)/(2^2 xx 5^3))^2 xx 25/27`
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Solution
We have, `((6 xx 10)/(2^2 xx 5^3))^2 xx 25/27 = ((2 xx 3 xx 2 xx 5)/(2^2 xx 5^3)) xx 5^2/3^3` ...[∵ 6 = 2 × 3 and 10 = 2 × 5]
= `((2^2 xx 3 xx 5)/(2^2 xx 5^3)) xx 5^2/3^3`
= `(3/5^2)^2 xx 5^2/3^3` ...[∵ (a × b)m = am × bm]
= `3^2/5^4 xx 5^2/3^3` ...[∵ (am)n = amn]
= `1/(5^2 xx 3)`
= `1/(25 xx 3)`
= `1/75`
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