Watch out
Multiplying indices when multiplying powers.
Scottish National 5 Mathematics
National 5 Maths Laws of indices
Use positive, negative and fractional indices in single and combined calculations.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Identify the common base.
- Be ready to work exactly without a calculator and show each mathematical step.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Laws of indices is an assessed part of Scottish National 5 Mathematics in the number area. Use positive, negative and fractional indices in single and combined calculations.
Identify the common base.
Choose the matching index law.
Apply the law before evaluating any numerical power.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Key formulae and rules
- am x an = am+n
- = am−n
- (am)n = amn
- a^ = nth root of am
Check
Check that the final exact form is fully simplified and follows the relevant square-factor or index law.
Exam tip
Show the number rule or multiplier used, retain exact values where requested and round only once at the end.
Worked examples
Worked example 1
Laws of indices worked example
Simplify
- For division, subtract the indices.
- 5 − (-2) = 7
Answer: x⁷
Watch out
- Multiplying indices when multiplying powers.
- Forgetting that subtracting a negative index adds.