Convert between radicals and rational exponents - Radicals

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.

Basic concepts:
Evaluating and simplifying radicals
Converting radicals to mixed radicals
Converting radicals to entire radicals
Combining the exponent rules

Related concepts:
Conversion between entire radicals and mixed radicals
Exponents: Rational exponents

Lessons

Notes:

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

- a)
  How to convert between radicals and rational exponents?
1.
Write the following in the radical form
2.
Write the answer with positive exponents and then as entire radical
3.
Write the answer as a power and evaluate

Convert between radicals and rational exponents

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AlgebraEvaluating and simplifying radicals

AlgebraConverting radicals to mixed radicals

AlgebraConverting radicals to entire radicals

AlgebraCombining the exponent rules

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Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Combining the exponent rules

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Intro Lesson:

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Lesson: 1a

Lesson: 1b

Lesson: 2a

Lesson: 2b

Lesson: 2c

Lesson: 3a

Lesson: 3b

Lesson: 3c

Lesson: 3d

Lesson: 3e

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Don't just watch, practice makes perfect.

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Don't just watch, practice makes perfect.

Lessons

Notes:

Ax/y=yAx {A^{x/y}} = {^y}\sqrt{A^x}Ax/y=yAx​

Intro Lesson

a)

How to convert between radicals and rational exponents?

1.

Write the following in the radical form

a)

27−23 {27^{- \frac{2}{3}}}27−32​

b)

(−8)−35(-8 {)^{- \frac{3}{5}}}(−8)−53​

2.

Write the answer with positive exponents and then as entire radical

a)

(94)−34( \frac{9}{4}{)^{- \frac{3}{4}}}(49​)−43​

b)

−(−16)−45 -(-16 {)^{- \frac{4}{5}}}−(−16)−54​

c)

(5x37)(25x−37) \frac{(5 {x^\frac{3}{7}} )}{(25 {x^{- \frac{3}{7}})}}(25x−73​)(5x73​)​

3.

Write the answer as a power and evaluate

a)

5a3{^5}\sqrt{a^3}5a3​

b)

381\sqrt{{^3}\sqrt{81}}381​​

c)

(43y)(33y) (4 {^3}\sqrt{y} )(3 {^3}\sqrt{y} )(43y​)(33y​)

d)

(43y−4)−3( {^4}\sqrt{3y-4} {)^{-3}}(43y−4​)−3

e)

−5(−x)3 - {^5}\sqrt{(-x{)^3}}−5(−x)3​

Convert between radicals and rational exponents

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

Algebra
Evaluating and simplifying radicals

Algebra
Converting radicals to mixed radicals

Algebra
Converting radicals to entire radicals

Algebra
Combining the exponent rules

or

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

${27^{- \frac{2}{3}}}$

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

$( \frac{9}{4}{)^{- \frac{3}{4}}}$

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

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

${^5}\sqrt{a^3}$

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

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

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

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