# How do you simplify sqrt(w^14)?

Sep 30, 2015

 = color(blue)(w^7

#### Explanation:

$\sqrt{{w}^{14}}$

Square root , can also be called as second root or a half power (color(blue)(1/2)

so , sqrt (w^14) = (w^14)^(color(blue)(1/2)

 = color(blue)(w^7

Oct 1, 2015

$\sqrt{{w}^{14}} = \left\mid {w}^{7} \right\mid$

#### Explanation:

If $a \ge 0$ then $\sqrt{{a}^{2}} = a$

If $a \ge 0$ and $b , c > 0$ then ${\left({a}^{b}\right)}^{c} = {a}^{b c}$

So if $w \ge 0$ then:

$\sqrt{{w}^{14}} = \sqrt{{\left({w}^{7}\right)}^{2}} = {w}^{7}$

and if $w < 0$ then:

$\sqrt{{w}^{14}} = \sqrt{{\left(- w\right)}^{14}} = \sqrt{{\left({\left(- w\right)}^{7}\right)}^{2}} = {\left(- w\right)}^{7} = - {w}^{7}$

So in both cases we have

$\sqrt{{w}^{14}} = \left\mid {w}^{7} \right\mid$