# Question 28a84

Sep 27, 2016

$\frac{{x}^{4}}{6 {y}^{8}}$

#### Explanation:

I am assuming that the expression is $\left(\frac{{x}^{4} / 3}{y} ^ 8\right) \cdot \frac{1}{2}$.

What we have here is ${x}^{4} / 3$ divided by ${y}^{8}$ and this result multiplied by $\frac{1}{2}$

That is (x^4/3÷y^8)1/2

When dividing fractions we change division to multiplication and tun the second fraction' upside down'

rArrx^4/3÷y^8/1=x^4/3xx1/y^8=x^4/(3y^8)#

Now multiply this result by $\frac{1}{2}$

$\Rightarrow {x}^{4} / \left(3 {y}^{8}\right) \times \frac{1}{2} = {x}^{4} / \left(6 {y}^{8}\right)$

Sep 27, 2016

Assuming that the question is supposed to read as ${\left({x}^{\frac{4}{3}} / {y}^{8}\right)}^{\frac{1}{2}}$

we can proceed in two ways...

Recall: ${x}^{\frac{1}{2}}$ is another way of writing a square root. $\sqrt{x}$

${\left({x}^{\frac{4}{3}} / {y}^{8}\right)}^{\frac{1}{2}} = \sqrt{\left({x}^{\frac{4}{3}} / {y}^{8}\right)}$

The square root of a fraction can be split...

$= \frac{\sqrt{\left({x}^{\frac{4}{3}}\right)}}{\sqrt{{y}^{8}}}$

To find the square root ... divide the index by 2.

$\frac{\sqrt{\left({x}^{\frac{4}{3}}\right)}}{\sqrt{{y}^{8}}} = {x}^{\frac{2}{3}} / {y}^{4}$

Recall: ${\left({x}^{m}\right)}^{n} = {x}^{m n} \text{ } \leftarrow$ multiply the indices

${\left({x}^{\frac{4}{3}} / {y}^{8}\right)}^{\frac{1}{2}} = {x}^{\frac{4}{3} \times \frac{1}{2}} / {y}^{8 \times \frac{1}{2}}$

=${x}^{\frac{2}{3}} / {y}^{4}$