# How do you simplify  (x+3)^(1/3) - (x+3)^(4/3) ?

Oct 18, 2015

$- {\left(x + 3\right)}^{\frac{1}{3}} \cdot \left(x + 2\right)$

#### Explanation:

You can simplify this expression by using ${\left(x + 3\right)}^{\frac{1}{3}}$ as a commonfactor.

Focusing solely on the exponents, you need to find the relationship between $\frac{1}{3}$, the exponent of the first term, and $\frac{4}{3}$, the exponent of the second term, so that

$\frac{1}{3} + \textcolor{red}{x} = \frac{4}{3} \implies \textcolor{red}{x} = \frac{4}{3} - \frac{1}{3} = \frac{3}{3} = 1$

If you use ${\left(x + 3\right)}^{\frac{1}{3}}$ as a common factor, you can thus write

${\left(x + 3\right)}^{\frac{1}{3}} \cdot \left[1 - {\left(x + 3\right)}^{\frac{3}{3}}\right] = {\left(x + 3\right)}^{\frac{1}{3}} \cdot \left[1 - {\left(x + 3\right)}^{1}\right]$

$= {\left(x + 3\right)}^{\frac{1}{3}} \cdot \left(1 - x - 3\right)$

$= \textcolor{g r e e n}{- {\left(x + 3\right)}^{\frac{1}{3}} \cdot \left(x + 2\right)}$