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:

[beautiful math coming... please be patient] $\sqrt{x} = x^{1/2}$

[beautiful math coming... please be patient] $\root 3\of{x} = x^{1/3}$

[beautiful math coming... please be patient] $\root 4\of{x} = x^{1/4}$

[beautiful math coming... please be patient] $\root 5\of{x} = x^{1/5}$

and so on!

Regardless of the name used, the normal restrictions apply.
For example, [beautiful math coming... please be patient] $\,x^{1/2}\,$ is only defined for [beautiful math coming... please be patient] $\,x\ge 0\,$.

EXAMPLES:

Write in rational exponent form:

[beautiful math coming... please be patient] $\root 7\of {x} = x^{1/7}$
[beautiful math coming... please be patient] $\sqrt{x^3} = (x^3)^{1/2} = x^{3/2}$
[beautiful math coming... please be patient] $\displaystyle\frac{1}{\sqrt{x}} = \frac{1}{x^{1/2}} = x^{-1/2}$
[beautiful math coming... please be patient] $\displaystyle\frac{3}{\root 5\of{x}} = \frac{3}{x^{1/5}} = 3x^{-1/5}$
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Writing Rational Exponents as Radicals

 
 
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
Write in rational exponent form:
(MAX is 12; there are 12 different problem types.)