WRITING RADICALS IN RATIONAL EXPONENT FORM

When serious work needs to be done with radicals,
they are usually changed to a name that uses exponents,
so that the exponent laws can be used.
Also, this new name for radicals allows them to be approximated on any calculator that has a power key.

Here are the rational exponent names for radicals:

$\sqrt{x} = x^{1/2}$

$\root 3\of{x} = x^{1/3}$

$\root 4\of{x} = x^{1/4}$

$\root 5\of{x} = x^{1/5}$

and so on!

Regardless of the name used, the normal restrictions apply.
For example, $\,x^{1/2}\,$ is only defined for $\,x\ge 0\,$.

EXAMPLES:

Write in rational exponent form:

$\root 7\of {x} = x^{1/7}$
$\sqrt{x^3} = (x^3)^{1/2} = x^{3/2}$
$\displaystyle\frac{1}{\sqrt{x}} = \frac{1}{x^{1/2}} = x^{-1/2}$
$\displaystyle\frac{3}{\root 5\of{x}} = \frac{3}{x^{1/5}} = 3x^{-1/5}$
Master the ideas from this section