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

**Citronette** · June 18th 2011, 08:55 AM

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

The answer provided is 10.

Any help is appreciated.

**Prove It** · June 18th 2011, 09:23 AM

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

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

**Citronette** · June 18th 2011, 10:51 PM

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

**earboth** · June 18th 2011, 11:07 PM

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.

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

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

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

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