Indices in algebra · Cambridge IGCSE Mathematics (9

In plain words

The rules for powers of numbers work just the same for letters. x³ × x⁴ means three x's times four x's, which is seven of them: x⁷. Numbers in front are multiplied or divided in the ordinary way.

Three things to know

x³ × x⁴ = x⁷ (add). x⁶ ÷ x² = x⁴ (subtract). (x²)³ = x⁶ (multiply).
Deal with the numbers in front separately: 3x² × 4x³ = 12x⁵.
A bracket's power applies to everything inside: (2x³)² = 4x⁶. And x⁻¹ = 1/x.

Worked example

Simplify (3x²y)³.

Cube the number: 3³ = 27.
Multiply each power by 3: x² becomes x⁶, and y becomes y³.
27x⁶y³.

Tips and tricks

In 3x² × 4x³, multiply the 3 and 4 but add the 2 and 3. Don't multiply the powers.
(2x)² is 4x², not 2x². The 2 gets squared too.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Indices in algebra: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What is x² × x⁵?
- x¹⁰
- x⁷ (the answer)
- 2x⁷
- x³
Add the powers.
What is y⁸ ÷ y²?
- y⁴
- y⁶ (the answer)
- y¹⁰
- y¹⁶
Subtract the powers.
What is (a³)⁴?
- a⁷
- a¹² (the answer)
- 4a³
- a⁸¹
Multiply the powers.
What is 2x × 3x²?
- 5x³
- 6x²
- 6x³ (the answer)
- 5x²
2 × 3 = 6, and x × x² = x³.
What is (5x²)²?
- 5x⁴
- 10x⁴
- 25x⁴ (the answer)
- 25x²
Square the 5 and double the power.

5 questions

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Worksheet

4 questions, 8 marks. Write your answers on paper, then check them.