Fractional and Negative Indices

Fractional and Negative Indices

by Joanne Casanova-Navalle

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​Objectives:

​- Work out expressions with fractional indices

​- Work out expressions with negative indices

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What are these numbers? Use a calculator!

What are these numbers? Use a calculator!

What are these numbers? Use a calculator!

What are these numbers? Use a calculator!

What are these numbers? Use a calculator!

What are these numbers? Use a calculator!

So from these examples we can see that...

Numbers raised to rational powers can be written as radicals or surds

What are these numbers? Use a calculator!

What are these numbers? Use a calculator!

What are these numbers? Use a calculator!

Fill in the Blanks

Work out:  $8^{\frac{1}{3}}$  

​EXAMPLE 1

​From Grade 9:

Multiple Choice

Work out:  $$8^{\frac{2}{3}}$$  

• 4

• 8

• 16

• 32

​EXAMPLE 2

Fill in the Blanks

Work out $\sqrt[3]{27^2}$  

​EXAMPLE 3

Multiple Choice

Work out:  $$\left(\frac{4}{25}\right)^{\frac{3}{2}}$$  

• $$\frac{8}{125}$$  

• $$\frac{125}{8}$$  

• $$\frac{2}{25}$$  

• $$\frac{25}{2}$$  

​EXAMPLE 4

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​NEGATIVE INDICES

​EXAMPLE 5

​EXAMPLE 5

​EXAMPLE 5

Multiple Choice

Work out:  $$8^{-\frac{2}{3}}$$  

• $$-\frac{1}{4}$$  

• $$-\frac{1}{2}$$  

• $$\frac{1}{2}$$  

• $$\frac{1}{4}$$  

​EXAMPLE 6

​EXAMPLE 6

​EXAMPLE 6

Multiple Choice

Work out:   $$\left(\frac{2}{3}\right)^{-2}$$  

• $$\frac{4}{9}$$  

• $$\frac{9}{4}$$  

• $$-\frac{4}{9}$$  

• $$-\frac{9}{4}$$  

​EXAMPLE 7

Multiple Choice

Work out: $$\left(\frac{16}{81}\right)^{-\frac{3}{4}}$$  

• $$-\frac{8}{27}$$  

• $$\frac{8}{27}$$  

• $$-\frac{27}{8}$$  

• $$\frac{27}{8}$$  

​EXAMPLE 8

Fill in the Blanks

What is the value of  $2^0?$  

​EXAMPLE 9

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LET US PRACTICE!

​5 QUESTIONS

Multiple Choice

Work out  $$4^{-1}$$  

• -4

• $$\frac{1}{4}$$  

• $$-\frac{1}{4}$$  

• $$\frac{3}{4}$$  

Multiple Choice

Work out  $$\left(\frac{3}{4}\right)^{-1}$$  

• $$-\frac{3}{4}$$  

• $$\frac{3}{4}$$  

• $$\frac{4}{3}$$  

• $$\frac{3}{4}$$  

Multiple Choice

Work out  $$\left(\frac{2}{3}\right)^{-3}$$  

• $$\frac{4}{9}$$  

• $$\frac{9}{4}$$  

• $$\frac{8}{27}$$  

• $$\frac{27}{8}$$  

Fill in the Blanks

What is the value of x in the equation $\left(\frac{5}{4}\right)^x=\frac{16}{25}$  ?

Fill in the Blanks

Work out  $9^{\frac{3}{2}}$  

​CLASSWORK

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