# Convert between radicals and rational exponents

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##### Intros
###### Lessons
1. How to convert between radicals and rational exponents?
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##### Examples
###### Lessons
1. Write the following in the radical form
1. ${27^{- \frac{2}{3}}}$
2. $(-8 {)^{- \frac{3}{5}}}$
2. Write the answer with positive exponents and then as entire radical
1. $( \frac{9}{4}{)^{- \frac{3}{4}}}$
2. $-(-16 {)^{- \frac{4}{5}}}$
3. $\frac{(5 {x^\frac{3}{7}} )}{(25 {x^{- \frac{3}{7}})}}$
3. Write the answer as a power and evaluate
1. ${^5}\sqrt{a^3}$
2. $1/ {^4}\sqrt{a^7}$
3. $\sqrt{{^3}\sqrt{81}}$
4. $(4 {^3}\sqrt{y} )(3 {^3}\sqrt{y} )$
5. $( {^4}\sqrt{3y-4} {)^{-3}}$
6. $- {^5}\sqrt{(-x{)^3}}$
###### Topic Notes
We will learn how to convert between radicals and rational exponents in this lesson. Therefore, it is a good idea to brush up on your understanding of all the basic rules of exponents before stating to watch the lesson.
${A^{x/y}} = {^y}\sqrt{A^x}$