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Question
Simplify:
`(3/5)^4 (8/5)^-12 (32/5)^6`
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Solution
`(3/5)^4 (8/5)^-12 (32/5)^6 = 3^4/5^4 xx (5/2^3)^12 xx (2^5/5)^6` ...`(∵ a^-1 = 1/a)`
= `3^4/5^4 xx 5^12/2^36 xx 2^30/5^6` ...[∵ (am)n = amn]
= `(3^4 xx 5^(12 - 4 - 6))/(2^(36 - 30))` ...`[∵ a^m/a^n = a^(m - n)]`
= `3^4/2^6 xx 5^2`
= `(81 xx 25)/64`
= `2025/64`
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