# How do you simplify 3 sqrt x^15?

Mar 3, 2016

$3 {x}^{\text{15/2}}$

#### Explanation:

Recall that a square root is the same as a $\text{1/2}$ power.

Thus,

$3 \sqrt{{x}^{15}} = 3 {\left({x}^{15}\right)}^{\text{1/2}}$

Now, use the rule:

${\left({a}^{b}\right)}^{c} = {a}^{b c}$

Multiply $15$ and $\text{1/2}$:

$= 3 {x}^{\text{15/2}}$

Mar 3, 2016

$3 {x}^{7} \sqrt{x}$

#### Explanation:

Try to rewrite ${x}^{15}$ in terms of squared terms.

${x}^{15} = {x}^{14} \cdot x = {\left({x}^{7}\right)}^{2} \cdot x$

Thus, we have

$3 \sqrt{{x}^{15}} = 3 \sqrt{{\left({x}^{7}\right)}^{2} \cdot x}$

The ${\left({x}^{7}\right)}^{2}$ term can be brought out of the square root term without the squared part.

$= 3 {x}^{7} \sqrt{x}$