Indices

An index (or power) is a short way to write a number multiplied by itself: $2^5$ means 2 × 2 × 2 × 2 × 2. In this topic you'll learn the index laws that make powers quick to multiply, divide and raise to a power, with numbers and with letters. You'll find out what a zero or negative index means, and use scientific notation to write and work with very large and very small measurements, from the distance to the Sun to the width of a red blood cell.

What you'll learn

• 2.01 Multiplication law: multiplying powers with the same base by adding the indices, including terms like $3x^2 \times 4x^5$.
• 2.02 Division law: dividing powers with the same base by subtracting the indices, including fractions like $\frac{12a^7}{4a^3}$.
• 2.03 Power of a power law: raising a power to a power by multiplying the indices, brackets like $(2x^3)^4$, and using all three laws together.
• 2.04 Zero and negative indices: why $a^0 = 1$, what $2^{-3}$ means, and writing answers with positive indices.
• 2.05 Scientific notation: writing very large and very small numbers like $1.5 \times 10^8$ and $7.5 \times 10^{-6}$, and calculating with them.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: smaller numbers and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: harder expressions and multi-step problems, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.