Learn Powers and Indices in GCSE Maths

Back to Maths

Tackle higher-tier powers: use index laws, work with negative and fractional indices, and compare sizes using standard form and orders of magnitude.

Explore the Topic →

(quiz starts below)

Fascinating Fact:

In astronomy, orders of magnitude compare huge distances, since 10⁹ metres = 1,000,000,000 metres, so moving the power by 1 multiplies or divides the size by 10.

In GCSE Maths, powers (indices) help you simplify expressions and handle very large or small numbers. You’ll apply the index laws, interpret negative and fractional indices, and use standard form to compare quantities efficiently.

Key Terms

Index (exponent): The power on a number, e.g., in a³ the 3 means a × a × a.
Order of magnitude: A power-of-ten estimate of size; each step of 10 indicates being about ten times bigger or smaller.
Standard form: Writing numbers as A × 10ⁿ with 1 ≤ |A| < 10 and integer n (also called scientific notation).

Frequently Asked Questions (Click to see answers)

What does a negative power mean?

A negative power means “put it on the bottom.” For example, a⁻³ = 1/a³.

How do I write a number in standard form?

Move the decimal so the first part is between 1 and 10, then multiply by a power of 10. Example: 12,500 = 1.25 × 10⁴.

How do I multiply and divide powers with the same base?

Add powers when multiplying: a^m × aⁿ = a^m+n. Subtract powers when dividing: a^m ÷ aⁿ = a^m−n.

Leave Feedback

Maths Quiz - Powers (H) (Questions)

Fascinating Fact:

Key Terms

Frequently Asked Questions (Click to see answers)

Try These Related Quizzes