WRITING RADICALS IN RATIONAL EXPONENT FORM

LESSON READ-THROUGH
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
 

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:

$\root 7\of {x} = x^{1/7}$
$\cssId{s19}{\sqrt{x^3}} \cssId{s20}{= (x^3)^{1/2}} \cssId{s21}{= x^{3/2}}$
$\displaystyle \cssId{s22}{\frac{1}{\sqrt{x}}} \cssId{s23}{= \frac{1}{x^{1/2}}} \cssId{s24}{= x^{-1/2}}$
$\displaystyle \cssId{s25}{\frac{3}{\root 5\of{x}}} \cssId{s26}{= \frac{3}{x^{1/5}}} \cssId{s27}{= 3x^{-1/5}}$
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
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
PROBLEM TYPES:
1 2 3 4 5 6 7 8 9 10 11 12
AVAILABLE MASTERED IN PROGRESS

Write in rational exponent form:
(MAX is 12; there are 12 different problem types.)