Question

Question #28a84

Answer 1

`(x^4)/(6y^8)`

Explanation:

I am assuming that the expression is `((x^4/3)/y^8) * 1/2`.

What we have here is `x^4/3` divided by `y^8` and this result multiplied by `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 `1/2`

`rArrx^4/(3y^8)xx1/2=x^4/(6y^8)`

Answer 2

Assuming that the question is supposed to read as `(x^(4/3)/y^8)^(1/2)`

we can proceed in two ways...

Recall: `x^(1/2)` is another way of writing a square root. `sqrtx`

`(x^(4/3)/y^8)^(1/2) = sqrt((x^(4/3)/y^8))`

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

`= sqrt((x^(4/3)))/sqrt(y^8)`

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

`sqrt((x^(4/3)))/sqrt(y^8) = x^(2/3)/y^4`

Recall: `(x^m)^n = x^(mn) " "larr` multiply the indices

`(x^(4/3)/y^8)^(1/2) = x^(4/3xx1/2)/y^(8xx1/2)`

=`x^(2/3)/y^4`