Question

`√(6) /√(27)`

Answer 1

`\mathrm{Apply\:the\:laws\:of\:exponents}:\quad (√(a))/(√(b))=\sqrt{(a)/(b )},\:\quad \:a\ge 0,\:b\ge 0`

`(√(6))/(√(27))=\sqrt{(6)/(27)}`

`=\sqrt{(6)/(27)}`

`\mathrm{ Cancel \ \ (6)/(27) \ \ \ ; \ \ (2)/(9) }`

`=\sqrt{(2)/(9)}`

`\mathrm{Apply\:the\:laws\:of\:exponents}:\quad \sqrt{(a)/(b)}=(√(a))/(√(b )),\:\quad \:a\ge 0,\:b\ge 0`

`=\sqrt{(2)/(9)}`

`√(9)=3`

`=(√(2))/(3) \ \ === > \ \ \ Answer`

`\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}`