Laws of Indices (Edexcel IAL Maths)

Spec point — 1.1

Laws of indices

What do I need to know about laws of indices?

• Laws of indices (or index laws – 'index' is the singular, 'indices' is the plural) allow you to simplify and manipulate expressions involving powers
• The index laws you need to know and use are summarised here:

How do I change the base of a term?

• Sometimes expressions involve different base values

• You can use index laws to change the base of a term to simplify an expression involving terms with different bases

  • For example $9^{4}=(3^{2})^{4}=3^{2\times4}=3^{8}$
  • Using the above can then help with problems like $9^{4}\div3^{7}=3^{8}\div3^{7}=3^{8-7}=3^{1}=3$

Exam Hint

• Index laws only work with terms that have the same base, so something like 2³× 5² cannot be simplified using index laws

Worked Example