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Still Confused?

Try reviewing these fundamentals first

Still Confused?

Try reviewing these fundamentals first

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Get Started Now- Intro Lesson6:50
- Lesson: 1a0:57
- Lesson: 1b1:04
- Lesson: 2a1:28
- Lesson: 2b1:33
- Lesson: 2c1:27
- Lesson: 3a0:32
- Lesson: 3b1:11
- Lesson: 3c0:58
- Lesson: 3d1:28
- Lesson: 3e1:04

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

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

- Introductiona)How to convert between radicals and rational exponents?
- 1.Write the following in the radical forma)${27^{- \frac{2}{3}}}$b)$(-8 {)^{- \frac{3}{5}}}$
- 2.Write the answer with positive exponents and then as entire radicala)$( \frac{9}{4}{)^{- \frac{3}{4}}}$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 evaluatea)${^5}\sqrt{a^3}$b)$\sqrt{{^3}\sqrt{81}}$c)$(4 {^3}\sqrt{y} )(3 {^3}\sqrt{y} )$d)$( {^4}\sqrt{3y-4} {)^{-3}}$e)$- {^5}\sqrt{(-x{)^3}}$

24.

Indices

24.1

Indices: Product rule $(a^x)(a^y)=a^{(x+y)}$

24.2

Indices: Division rule ${a^x \over a^y}=a^{(x-y)}$

24.3

Indices: Power rule $(a^x)^y = a^{(x\cdot y)}$

24.4

Indices: Negative exponents

24.5

Indices: Zero exponent: $a^0 = 1$

24.6

Indices: Rational exponents

24.7

Combining laws of indices

24.8

Scientific notation

24.9

Convert between radicals and rational exponents

24.10

Solving for indices

We have over 1640 practice questions in AU Maths Extension 1 for you to master.

Get Started Now24.1

Indices: Product rule $(a^x)(a^y)=a^{(x+y)}$

24.2

Indices: Division rule ${a^x \over a^y}=a^{(x-y)}$

24.3

Indices: Power rule $(a^x)^y = a^{(x\cdot y)}$

24.4

Indices: Negative exponents

24.6

Indices: Rational exponents

24.7

Combining laws of indices

24.8

Scientific notation

24.9

Convert between radicals and rational exponents

24.10

Solving for indices