# Question c2af6

Nov 13, 2017

$35 {x}^{6}$

#### Explanation:

color(blue)((49x^6)^(1/2)xx(125x^9)^(1/3)

To solve this we use three rules

o. color(brown)((xy)^z=z^zy^z

o. color(brown)((x^y)^z=x^(yz)

o. color(brown)(x^yxxx^z=x^(y+z)

So, lets find the solution

$\rightarrow {\left(49 {x}^{6}\right)}^{\frac{1}{2}} \times {\left(125 {x}^{9}\right)}^{\frac{1}{3}}$

Use color(brown)((xy)^z=z^zy^z

$\rightarrow {\left(49\right)}^{\frac{1}{2}} \times {\left({x}^{6}\right)}^{\frac{1}{2}} \times {\left(125\right)}^{\frac{1}{3}} \times {\left({x}^{9}\right)}^{\frac{1}{3}}$

$\rightarrow {\left(7 \times 7\right)}^{\frac{1}{2}} \times {\left({x}^{6}\right)}^{\frac{1}{2}} \times {\left(5 \times 5 \times 5\right)}^{\frac{1}{3}} \times {\left({x}^{9}\right)}^{\frac{1}{3}}$

$\rightarrow {\left({7}^{2}\right)}^{\frac{1}{2}} \times {\left({x}^{6}\right)}^{\frac{1}{2}} \times {\left({5}^{3}\right)}^{\frac{1}{3}} \times {\left({x}^{9}\right)}^{\frac{1}{3}}$

Use color(brown)((x^y)^z=x^(yz)

$\rightarrow {\left(7\right)}^{\left(2\right) \left(\frac{1}{2}\right)} \times {\left(x\right)}^{\left(6\right) \left(\frac{1}{2}\right)} \times {\left(5\right)}^{\left(3\right) \left(\frac{1}{3}\right)} \times {\left(x\right)}^{\left(9\right) \left(\frac{1}{3}\right)}$

$\rightarrow 7 \times {x}^{3} \times 5 \times {x}^{3}$

Use color(brown)(x^yxxx^z=x^(y+z)

color(green)(rArr35x^6#

Hope this helps!!! ☺☻