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

Apr 10, 2015

Things to remember
$\sqrt{{y}^{3}} = {\left(\sqrt{y}\right)}^{3}$
$\sqrt{a} = {a}^{\frac{1}{2}}$
and
${\left({p}^{q}\right)}^{r} = {p}^{q r}$

Therefore
(4)sqrt(y^3))

$= \left(4\right) {\left(\sqrt{y}\right)}^{3}$

$= \left(4\right) {\left({y}^{\frac{1}{2}}\right)}^{3}$

$= 4 {y}^{\frac{3}{2}}$

Apr 10, 2015

4y^$\left(\frac{3}{2}\right)$

Square root means exponent is $\frac{1}{2}$ of every number inside the radical sign. Hence the exponent 3 would become $\frac{3}{2}$ when radical sign is dispensed with.