# Laws of indices

Rules for combining powers. Add the powers when multiplying, subtract when dividing, and multiply them for a power of a power.

Maths (school) · Part 01: Number and ratio · Card 7 of 9 · Last updated 2026-10-19

## Analogy

Like stacking blocks: 2^3 is three twos, 2^4 is four twos, so together you have seven twos.

## Example

**Same base**

2^3 x 2^4 = 2^7 = 128
5^6 / 5^4 = 5^2 = 25
(3^2)^3 = 3^6 = 729

## In practice

Computer memory sizes such as 2^10 = 1,024 rely on these rules.

## Practice

### Flashcards

- **What is 2^3 x 2^4 as a single power?** 2^7. When multiplying powers of the same base, add the indices.

## Questions people ask

### What does a negative power mean?

A negative power means 'one over' the positive power. So 2^-3 = 1/2^3 = 1/8. It does not make the answer negative. It flips the number to the bottom of a fraction. A power of zero is always 1. For example, 10^-2 is 1/100, which is 0.01. Negative powers are how very small numbers are written.

### Why is any number to the power 0 equal to 1?

Use the division rule. 5^3 / 5^3 = 5^0, but any number divided by itself is 1. So 5^0 = 1. The same logic works for every number except zero, which gives no sensible answer. For example, 10^3 / 10^3 = 1000 / 1000 = 1, which is also 10^0. The rule keeps all the index laws working together.

## Related concepts

- [Standard form](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-8)
- [BIDMAS](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-1)
- [Adding fractions](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-2)
- [Percentage of an amount](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-3)

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