# Thread: check on working : (5 ^1/4 x 2 ^ 1/6)^2 / 5^-1/2 x 2 ^ 2/3

1. ## check on working : (5 ^1/4 x 2 ^ 1/6)^2 / 5^-1/2 x 2 ^ 2/3

Hi,

I was wondering if there is anything wrong with the working for the question above:

my working
(5 ^1/4 x 2 ^ 1/6)^2 / 5^-1/2 x 2 ^ 2/3

= (5 ^ [1/4 x 2]) x (2 ^ [1/6 x 2]) / 5 ^-1/2 x 2 ^2/3

= 5 ^ 1/2 x 2 ^ 1/3 / 5 ^-1/2 x 2 ^2/3

= 5 ^ [1/2 -(-1/2)] x 2 ^ (1/3 - 2/3)

= 5 x 2 ^ -1/3

= 5 / 2 ^3

= 5 / 8

Any help is appreciated.

2. ## Re: check on working : (5 ^1/4 x 2 ^ 1/6)^2 / 5^-1/2 x 2 ^ 2/3

This is almost unreadable. Assuming that your question is to simplify $\displaystyle \frac{\left(5^{\frac{1}{4}}\cdot 2^{\frac{1}{6}}\right)^2}{5^{-\frac{1}{2}}\cdot 2^{\frac{2}{3}}}$, then

\displaystyle \begin{align*} \frac{\left(5^{\frac{1}{4}}\cdot 2^{\frac{1}{6}}\right)^2}{5^{-\frac{1}{2}}\cdot 2^{\frac{2}{3}}} &= \frac{\left(5^{\frac{1}{4}}\right)^2\cdot \left(2^{\frac{1}{6}}\right)^2}{5^{-\frac{1}{2}}\cdot 2^{\frac{2}{3}}} \\ &= \frac{5^{\frac{1}{2}}\cdot 2^{\frac{1}{3}}}{5^{-\frac{1}{2}} \cdot 2^{\frac{2}{3}}} \\ &= 5^{\frac{1}{2} - \left(-\frac{1}{2}\right)} \cdot 2^{\frac{1}{3} - \frac{2}{3}} \\ &= 5^1 \cdot 2^{-\frac{1}{3}} \\ &= \frac{5}{2^{\frac{1}{3}}} \\ &= \frac{5}{\sqrt[3]{2}} \end{align*}

3. ## Re: check on working : (5 ^1/4 x 2 ^ 1/6)^2 / 5^-1/2 x 2 ^ 2/3

Hi Thanks for checking my working. I'll type my working out in photoshop and post it as an image next time.

4. ## Re: check on working : (5 ^1/4 x 2 ^ 1/6)^2 / 5^-1/2 x 2 ^ 2/3

Originally Posted by Citronette
Hi Thanks for checking my working. I'll type my working out in photoshop and post it as an image next time.
Hello,

why don't you use some LaTeX as it is usual here at MHF?

Have a look here: http://www.mathhelpforum.com/math-he...ial-19060.html

If you want to know how Prove It wrote the quotient move the mouse cursor over the formula and you'll see the code.