# How do you simplify (9n^4)^(1/2)?

$3 {n}^{2}$

#### Explanation:

We can distribute the fractional exponent through the expression:

${\left(9 {n}^{4}\right)}^{\frac{1}{2}} = {9}^{\frac{1}{2}} \times {\left({n}^{4}\right)}^{\frac{1}{2}}$

I'm going to rewrite $9 = {3}^{2}$

${\left({3}^{2}\right)}^{\frac{1}{2}} \times {\left({n}^{4}\right)}^{\frac{1}{2}}$

We can now use the rule that ${\left({x}^{a}\right)}^{b} = {x}^{a b}$

${3}^{2 \times \left(\frac{1}{2}\right)} \times {n}^{4 \times \left(\frac{1}{2}\right)}$

${3}^{1} \times {n}^{2} = 3 {n}^{2}$