Show that : `(i)root(3)729/root(3)1000=root(3)(729/1000)` (ii) `root3( (-512 )/(343))= root3 (-512)/root3 (343)`

Explanation

`(i)root(3)729/root(3)1000=root(3)(729/1000)`
`=>root3(9 xx 9 xx 9)/root3(10 xx 10 xx 10)=root3((9 xx 9 xx 9)/(10 xx 10 xx 10))`

`=>9/10=root3(9^3/10^3)`

`=>9/10=(9^3)^1/3/(10^3)^1/3`

`=>therefore 9/10=9/10`


`(ii)root3(-512)/root3(343)=root(3)(-512/343)`

`=>-root3(8 xx 8 xx 8)/root3(7xx 7 xx 7)=-root3((8 xx 8 xx 8)//(7xx 7 xx 7))`

`=>-8/7=-root3(8^3/7^3)`

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