# Math Help - Exponent simplification

1. ## 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?

2. ## Re: Exponent simplification

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*}

3. ## 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.

4. ## Re: Exponent simplification

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

5. ## 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.

6. ## Re: Exponent simplification

Look in the LaTeX help subforum on this site.

7. ## Re: Exponent simplification

Found it. Thanks Prove It.