Exponent simplification

• Nov 19th 2012, 07:38 AM
Greymalkin
Exponent simplification
should be easy(for you):
$\displaystyle \frac{8}{27}(\frac{9}{4}x-\frac{5}{4})^\frac{3}{2}$

becomes

$\displaystyle \frac{1}{27}(9x-5)^\frac{3}{2}$

through what operations?
• Nov 19th 2012, 07:47 AM
Prove It
Re: Exponent simplification
Quote:

Originally Posted by Greymalkin
should be easy(for you):
$\displaystyle \frac{8}{27}(\frac{9}{4}x-\frac{5}{4})^\frac{3}{2}$

becomes

$\displaystyle \frac{1}{27}(9x-5)^\frac{3}{2}$

through what operations?

\displaystyle \displaystyle \begin{align*} \frac{8}{27} \left( \frac{9}{4} \, x - \frac{5}{4} \right) ^{\frac{3}{2}} &= \frac{8}{27} \left( \frac{9x - 5}{4} \right)^{\frac{3}{2}} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{4^{\frac{3}{2}}} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{\left( 4^{\frac{1}{2}} \right)^3} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{2^3} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{8} \\ &= \frac{1}{27} \left( 9x - 5 \right)^{\frac{3}{2}} \end{align*}
• Nov 19th 2012, 07:52 AM
RBowman
Re: Exponent simplification
Hi Grey.

8/27 * (9/4 x - 5/4) ^ 3/2 =
8/27 * [1/4 (9 x - 5)] ^ 3/2 =
8/27 * (1/4) ^ 3/2 * (9 x - 5) ^ 3/2 =
8/27 * 1/8 * (9 x - 5) ^ 3/2 =
1/27 * (9 x - 5) ^ 3/2.

Hope that helps. I'll learn to typeface soon. I'm still new to the forum.
• Nov 19th 2012, 07:57 AM
Prove It
Re: Exponent simplification
Quote:

Originally Posted by RBowman
Hi Grey.

8/27 * (9/4 x - 5/4) ^ 3/2 =
8/27 * [1/4 (9 x - 5)] ^ 3/2 =
8/27 * (1/4) ^ 3/2 * (9 x - 5) ^ 3/2 =
8/27 * 1/8 * (9 x - 5) ^ 3/2 =
1/27 * (9 x - 5) ^ 3/2.

Hope that helps. I'll learn to typeface soon. I'm still new to the forum.

Hopefully you'll learn to type faster as well, I beat you by a full five minutes, even when using LaTeX :P lol
• Nov 19th 2012, 08:02 AM
RBowman
Re: Exponent simplification
I am a bit jealous. You wanna help by pointing me to best thread in the forum for users getting started with LaTeX? I'm also slow when it comes to finding things on my own. :)
• Nov 19th 2012, 08:03 AM
Prove It
Re: Exponent simplification
Look in the LaTeX help subforum on this site.
• Nov 19th 2012, 08:04 AM
RBowman
Re: Exponent simplification
Found it. Thanks Prove It.