Exponent simplification

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November 19th 2012, 07:38 AM
Greymalkin

Exponent simplification

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

becomes

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

through what operations?
November 19th 2012, 07:47 AM
Prove It

Re: Exponent simplification

Quote:

Originally Posted by Greymalkin

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

becomes

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

through what operations?

$\displaystyle \begin{align*} \frac{8}{27} \left( \frac{9}{4} \, x - \frac{5}{4} \right) ^{\frac{3}{2}} &= \frac{8}{27} \left( \frac{9x - 5}{4} \right)^{\frac{3}{2}} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{4^{\frac{3}{2}}} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{\left( 4^{\frac{1}{2}} \right)^3} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{2^3} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{8} \\ &= \frac{1}{27} \left( 9x - 5 \right)^{\frac{3}{2}} \end{align*}$
November 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.
November 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
November 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. :)
November 19th 2012, 08:03 AM
Prove It

Re: Exponent simplification

Look in the LaTeX help subforum on this site.
November 19th 2012, 08:04 AM
RBowman

Re: Exponent simplification

Found it. Thanks Prove It.