# How do you simplify \sqrt { ( 729x ^ { \frac { 3} { 4} } ) ^ { \frac { 1} { 3} } }?

##### 1 Answer
Sep 9, 2017

$3 {x}^{\frac{1}{8}}$

#### Explanation:

$\sqrt{{\left(729 {x}^{\frac{3}{4}}\right)}^{\frac{1}{3}}}$

sqrt((729^(1/3) xx x^(3/4 xx 1/3))

sqrt((729^(1/3) xx x^(cancel3/4 xx 1/cancel3))

$\sqrt{{729}^{\frac{1}{3}} \times {x}^{\frac{1}{4}}}$

$\sqrt{{\left({27}^{2}\right)}^{\frac{1}{3}} \times {x}^{\frac{1}{4}}}$

$\sqrt{{27}^{2 \times \frac{1}{3}} \times {x}^{\frac{1}{4}}}$

$\sqrt{{27}^{\frac{2}{3}} \times {x}^{\frac{1}{4}}}$

Recall $\to \sqrt{a} = {a}^{\frac{1}{2}}$

$\rightarrow {\left({27}^{\frac{2}{3}} \times {x}^{\frac{1}{4}}\right)}^{\frac{1}{2}}$

$\Rightarrow \left({27}^{\frac{2}{3} \times \frac{1}{2}} \times {x}^{\frac{1}{4} \times \frac{1}{2}}\right)$

$\Rightarrow \left({27}^{\frac{\cancel{2}}{3} \times \frac{1}{\cancel{2}}} \times {x}^{\frac{1}{8}}\right)$

$\Rightarrow \left({27}^{\frac{1}{3}} \times {x}^{\frac{1}{8}}\right)$

$\Rightarrow \left({\left({3}^{3}\right)}^{\frac{1}{3}} \times {x}^{\frac{1}{8}}\right)$

$\Rightarrow \left({3}^{3 \times \frac{1}{3}} \times {x}^{\frac{1}{8}}\right)$

$\Rightarrow \left({3}^{\cancel{3} \times \frac{1}{\cancel{3}}} \times {x}^{\frac{1}{8}}\right)$

$\Rightarrow \left({3}^{1} \times {x}^{\frac{1}{8}}\right)$

$\Rightarrow 3 {x}^{\frac{1}{8}}$