Indices, Powers & Roots

Overview

A power tells you how many times to multiply a number by itself: 3⁴ means 3 × 3 × 3 × 3. In Year 8 students move beyond squares and cubes to use index notation confidently, find square and cube roots, and learn the laws of indices that let you multiply and divide powers quickly. These rules are the gateway to standard form and to all of the algebra that follows.

What You Will Learn

• Use index notation to write and evaluate powers of positive integers
• Recognise and find square numbers, cube numbers and their roots
• Use the laws of indices to multiply and divide powers of the same base
• Evaluate expressions involving powers, including the power of zero
• Estimate the square root of a number that is not a perfect square

Key Vocabulary

Common Mistakes to Avoid

• Working out 3⁴ as 3 × 4 = 12 instead of 3 × 3 × 3 × 3 = 81
• Adding the bases when multiplying powers (2³ × 2² is 2⁵, not 4⁵)
• Thinking the square root of a number has only one value, or that √20 is a whole number
• Writing 5⁰ = 0 instead of 5⁰ = 1

Frequently Asked Questions