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Show that (-216)/(42875) is the cube of ...

Show that `(-216)/(42875)` is the cube of a rational number. Also find the rational number.

Text Solution

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Resolving `216` and `42875` into prime factor
`216`=`2xx2xx2xx3xx3xx3`
`42875`=`5xx5xx5xx7xx7xx7`
`216` and `42875` can be grouped into triples of equal factors
`(216)`=`(2xx3)^3`
`(42875)`=`(5xx7)^3`
Therefor,
`(-216/42875)`
`(-6)^3/(35)^3`
`(-216/42875)`is the cube root of ration number
`(-6/35)`
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