# Convert between radicals and rational exponents

### Convert between radicals and rational exponents

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.

#### Lessons

${A^{x/y}} = {^y}\sqrt{A^x}$

• Introduction
a)
How to convert between radicals and rational exponents?

• 1.
Write the following in the radical form
a)
${27^{- \frac{2}{3}}}$

b)
$(-8 {)^{- \frac{3}{5}}}$

• 2.
a)
$( \frac{9}{4}{)^{- \frac{3}{4}}}$

b)
$-(-16 {)^{- \frac{4}{5}}}$

c)
$\frac{(5 {x^\frac{3}{7}} )}{(25 {x^{- \frac{3}{7}})}}$

• 3.
Write the answer as a power and evaluate
a)
${^5}\sqrt{a^3}$

b)
$1/ {^4}\sqrt{a^7}$

c)
$\sqrt{{^3}\sqrt{81}}$

d)
$(4 {^3}\sqrt{y} )(3 {^3}\sqrt{y} )$

e)
$( {^4}\sqrt{3y-4} {)^{-3}}$

f)
$- {^5}\sqrt{(-x{)^3}}$