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Question
Simplify:
`((25)^(3/2)xx(243)^(3/5))/((16)^(5/4)xx(8)^(4/3))`
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Solution
Given `((25)^(3/2)xx(243)^(3/5))/((16)^(5/4)xx(8)^(4/3))`
`((25)^(3/2)xx(243)^(3/5))/((16)^(5/4)xx(8)^(4/3))=(5^(2xx3/2)xx3^(5xx3/5))/(2^(4xx5/4)xx2^(3xx4/3))`
`=(5^3xx3^3)/(2^5xx2^4)`
`=(125xx27)/(32xx16)`
`=3375/512`
Hence the value of `((25)^(3/2)xx(243)^(3/5))/((16)^(5/4)xx(8)^(4/3))` is `3375/512`
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