# How do you rewrite with fractional exponents for sqrt((4mn)/(a^2b^2))?

Mar 6, 2018

$\frac{2 {\left(m n\right)}^{\frac{1}{2}}}{a b}$

#### Explanation:

Since we say that $\sqrt{x} = {x}^{\frac{1}{2}}$, we can write the above as:

${\left(4 m n\right)}^{\frac{1}{2}} / {\left({a}^{2} {b}^{2}\right)}^{\frac{1}{2}}$

Since ${\left(x y\right)}^{z} = {x}^{z} {y}^{z}$, we can write:

$\frac{{4}^{\frac{1}{2}} {m}^{\frac{1}{2}} {n}^{\frac{1}{2}}}{{\left({a}^{2}\right)}^{\frac{1}{2}} {\left({b}^{2}\right)}^{\frac{1}{2}}}$

Some of these cancel out:

$\frac{2 {m}^{\frac{1}{2}} {n}^{\frac{1}{2}}}{a b}$, and to make this look nicer, we can write:

$\frac{2 {\left(m n\right)}^{\frac{1}{2}}}{a b}$