Mathematics
Indices
Class 7
Intermediate
About 12 min
Premium
Laws of indices: add, subtract or multiply
Multiply, divide and raise powers of 2. See each written out in full, then find the shortcut: add the indices, subtract them or multiply them.
Core concept
For the same base, aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ and (aᵐ)ⁿ = aᵐⁿ
Topic: Indices
Powers of the same base follow three simple laws. Multiply: 2³ × 2² = (2 × 2 × 2) × (2 × 2) = 2⁵, so you add the indices: aᵐ × aⁿ = aᵐ⁺ⁿ. Divide: 2⁵ ÷ 2² cancels two twos, leaving 2³, so you subtract: aᵐ ÷ aⁿ = aᵐ⁻ⁿ. Power of a power: (2³)² = 2³ × 2³ = 2⁶, so you multiply: (aᵐ)ⁿ = aᵐⁿ. The laws work only when the base is the same. In this lab the base is 2, and you can check every answer by writing the powers out in full.
What you will learn
- State the three laws of indices.
- Simplify products, quotients and powers of powers with the same base.
- Check a law by writing the powers out in full.
Before you start
- Know what a base and an index are.
Materials
- None
Equipment
- A calculator to check
Procedure
- Record 2³ × 2².
- Record 2⁵ ÷ 2².
- Record (2³)².
- Record 2⁶ × 2³.
How this simulation is simplified
- The base is always 2.