# Math Help - basic simplification question

1. ## basic simplification question

is this right?

$\frac{cos(x)}{(cos^4(x))^{\frac{3}{2}}} = cos^{-5}(x)$

2. Looks good to me. Just a matter of using your power laws.

3. Looks good to me too.

4. Originally Posted by lllll
I need some help simplifying:

$\frac{cos(x)}{(cos^2(x))^{\frac{3}{2}}}$

$(\cos^2(x))^{3/2}=|cos(x)|^3$

so we get

$\begin{cases}
\sec^2(x) \mbox{if }-\frac{\pi}{2} < x < \frac{\pi}{2} \\
-\sec^2(x) \mbox{if } \frac{\pi}{2} < x < \frac{3\pi}{2}
\end{cases}$

5. $(\cos^4(x))^{3/2}=|cos(x)|^6$

Dont forget that

$\sqrt{x^2}=|x|$

example x=-2

Yours should be

$\frac{1}{|\cos(x)|\cos^4(x)}$

try $x=\pi$