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?
$\displaystyle \displaystyle \begin{align*} \frac{8}{27} \left( \frac{9}{4} \, x - \frac{5}{4} \right) ^{\frac{3}{2}} &= \frac{8}{27} \left( \frac{9x - 5}{4} \right)^{\frac{3}{2}} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{4^{\frac{3}{2}}} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{\left( 4^{\frac{1}{2}} \right)^3} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{2^3} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{8} \\ &= \frac{1}{27} \left( 9x - 5 \right)^{\frac{3}{2}} \end{align*}$
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.