Answer
$\displaystyle \frac{4}{3}x^{2}+\frac{1}{6}x^{3/2}- \displaystyle \frac{2}{3}x^{-2}$
Work Step by Step
Exponent form:
An expression is in exponent form if
* there are no radicals and
* all powers of unknowns occur in the numerator.
All terms in a sum or difference are of the form:
(constant)(expression with x$)^{p}$
-----------------
First term: no adjustments, $\displaystyle \quad \frac{4}{3}x^{2}$
Second term: no adjustments, $\displaystyle \quad \frac{1}{6}x^{3/2}$
Third term:
x is in the denominator, apply $a^{-n}=\displaystyle \frac{1}{a^{n}}=(\frac{1}{a})^{n}$
so it becomes$\quad \displaystyle \frac{2}{3}\cdot x^{-2}$
The expression, in exponent form is
$\displaystyle \frac{4}{3}x^{2}+\frac{1}{6}x^{3/2}- \displaystyle \frac{2}{3}x^{-2}$
