# How do you simplify this expression?

## $\frac{{\left(2 a\right)}^{\frac{1}{2}} {\left(3 b\right)}^{-} 2 {\left(4 a\right)}^{\frac{3}{5}}}{{\left(4 a\right)}^{- \frac{3}{2}} {\left(3 b\right)}^{2} {\left(2 a\right)}^{\frac{1}{5}}}$

Jan 27, 2018

$\frac{{2}^{\frac{9}{2}} {a}^{\frac{12}{5}}}{81 {b}^{4}}$

#### Explanation:

well, I think we can simplify this a bit.
$\frac{{\left(2 a\right)}^{\frac{1}{2}} {\left(3 b\right)}^{-} 2 {\left(4 a\right)}^{\frac{3}{5}}}{{\left(4 a\right)}^{- \frac{3}{2}} {\left(3 b\right)}^{2} {\left(2 a\right)}^{\frac{1}{5}}}$

lets take all the common bases together,

$\frac{{\left(2 a\right)}^{\frac{1}{2} - \frac{1}{5}} {\left(4 a\right)}^{\frac{3}{5} + \frac{3}{2}}}{{\left(3 b\right)}^{2 + 2}}$

$\frac{{\left(2 a\right)}^{\frac{3}{10}} {\left(4 a\right)}^{\frac{21}{10}}}{{\left(3 b\right)}^{4}}$

$\frac{{\left(2 a\right)}^{\frac{3}{10}} {\left(2 \cdot 2 a\right)}^{\frac{21}{10}}}{{\left(3 b\right)}^{4}}$

$\frac{{\left(2 a\right)}^{\frac{3}{10}} {2}^{\frac{21}{10}} {\left(2 a\right)}^{\frac{21}{10}}}{{\left(3 b\right)}^{4}}$

$\frac{{2}^{\frac{21}{10}} {\left(2 a\right)}^{\frac{12}{5}}}{{\left(3 b\right)}^{4}}$

that's the simplest I could get it to, I hope there are no errors, cuz it took a lot of typing. :)

-Sahar

I see that we can go one step further and remove the brackets.

$\frac{{2}^{\frac{21}{10}} {\left(2 a\right)}^{\frac{12}{5}}}{{\left(3 b\right)}^{4}} = \frac{{2}^{\frac{21}{10}} {\left(2 \cdot a\right)}^{\frac{12}{5}}}{{\left(3 \cdot b\right)}^{4}} = \frac{{2}^{\frac{21}{10}} {2}^{\frac{12}{5}} {a}^{\frac{12}{5}}}{{3}^{4} {b}^{4}}$

$\frac{{2}^{\frac{9}{2}} {a}^{\frac{12}{5}}}{81 {b}^{4}}$

EZ as pi