Still Confused?

Try reviewing these fundamentals first.

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Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

Nope, I got it.

That's that last lesson.

Start now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started Now- Lesson: 1a0:57
- Lesson: 1b1:04
- Lesson: 2a1:28
- Lesson: 2b1:33
- Lesson: 2c1:27
- Lesson: 3a0:32
- Lesson: 3c1:11
- Lesson: 3d0:58
- Lesson: 3e1:28
- Lesson: 3f1:04

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,

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

- 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)$1/ {^4}\sqrt{a^7}$c)$\sqrt{{^3}\sqrt{81}}$d)$(4 {^3}\sqrt{y} )(3 {^3}\sqrt{y} )$e)$( {^4}\sqrt{3y-4} {)^{-3}}$f)$- {^5}\sqrt{(-x{)^3}}$

23.

Indices

23.1

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

23.2

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

23.3

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

23.4

Indices: Negative exponents

23.5

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

23.6

Indices: Rational exponents

23.7

Combining laws of indices

23.8

Scientific notation

23.9

Convert between radicals and rational exponents

23.10

Solving for indices

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

Get Started Now23.1

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

23.2

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

23.3

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

23.4

Indices: Negative exponents

23.6

Indices: Rational exponents

23.7

Combining laws of indices

23.8

Scientific notation

23.9

Convert between radicals and rational exponents

23.10

Solving for indices