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Auralith Learning

Year 8 · Maths · Indices and standard form · Lesson 1

The laws of indices

Use index notation and the laws of indices to multiply, divide and raise powers, with numbers and letters, including the zero power.

Whiteboard video lesson: The laws of indices

23-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Evaluate powers
  • Multiply powers with the same base
  • Divide powers with the same base
  • Find a power of a power
  • Understand the zero index

The method

  1. Multiply: add the powers (same base only).
  2. Divide: subtract the powers.
  3. Power of a power: multiply the powers.
  4. Anything to the power 0 is 1.

Key words: index, power, base, index laws, simplify.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

Work out 3⁴.

  1. Step 1: 3⁴ = 3 × 3 × 3 × 3
  2. Step 2: = 9 × 3 × 3
  3. Step 3: = 81

Answer: 81

Question 2

Work out 10⁵.

  1. Step 1: 10⁵ = 10 × 10 × 10 × 10 × 10
  2. Step 2: = 100 × 10 × 10 × 10
  3. Step 3: = 100000

Answer: 100000

Question 3

Write as a single power: 2³ × 2⁶

  1. Step 1: Same base (2): add the powers
  2. Step 2: 3 + 6 = 9

Answer: 2⁹