MATHEMATICSTypes of Number – Indices

Aims of the Lesson

• To learn about indices.

Review

• You have already come across two powers or indices.

• When the power of 2 is indicated you are ‘squaring’ a number.

• When the power of 3 is indicated you are ‘cubing’ a number.

Symbol

• A power or index is the small number in the top right hand corner of a base or root value.

Bp

Base or Root

Index or Power

Positive Index or Power

• A positive index or power tells you how many times to multiply the base or root value by itself.

• E.g. 25 means 2 × 2 × 2 × 2 × 2

Index Form and Evaluation

• If you are asked to ‘evaluate’ you need to calculate the answer to the repeated multiplication.

• E.g. Evaluate 25 2 × 2 × 2 × 2 × 2 = 32

• If you are asked to write something in ‘index form’, you need to use the power shorthand or symbol to represent the repeated multiplication.

• E.g. 6 × 6 × 6 in index form = 63

BEWARE

• Remember powers relate to multiplication only and it must be the same number being multiplied each time so…

• 8 + 8 + 8 is NOT 83 but it is the same as 3 × 8

• 2 × 4 × 5 × 3 cannot be written in index form other than to give each value the power of 1, i.e. 21 × 41 × 51 × 31

• 3 × 7 × 3 is the same as 3 × 3 × 7 which can be simplified to 32 × 7

What next?

Learn how to use your calculator to calculate higher powers of larger and smaller values and learn about higher roots by...

…Working through the MyMaths lesson (and then its online homework) called:Number > Powers and Roots > Higher Powers

Save and complete the worksheet Index-S1.xlsx