Question

How do you write with fractional exponents for `(4)(sqrt(y^3))`?

Answer 1

Things to remember
`sqrt(y^3) = (sqrt(y))^3`
`sqrt(a) = a^(1/2)`
and
`(p^q)^r = p^(qr)`

Therefore
`(4)sqrt(y^3))`

`= (4) (sqrt(y))^3`

`= (4) (y^(1/2))^3`

`= 4 y ^(3/2)`

Answer 2

4y^`(3/2)`

Square root means exponent is `1/2` of every number inside the radical sign. Hence the exponent 3 would become `3/2` when radical sign is dispensed with.