Indices in algebra
Objective. Use index notation and multiply simple algebraic powers.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Indices in algebra extend index notation to letters, using the same laws as numerical powers to combine terms efficiently. When multiplying powers of the same base, add the indices, so a³ × a² = a⁵, and when dividing, subtract the indices, so a⁵ ÷ a² = a³. A power raised to another power multiplies the indices, so (a²)³ = a⁶. These rules only work directly when the bases are identical; different letters like a and b cannot be combined this way. Checking a small numerical example, such as a = 2, helps confirm a law has been applied correctly.
Worked example
Simplify x⁴ × x³ using the laws of indices in algebra.
- 1Identify that the bases are the same: x
- 2Apply the multiplication law by adding the indices: 4 + 3
- 3Write the simplified power: x⁷
- 4Check with x = 2: 2⁴ × 2³ = 16 × 8 = 128, and 2⁷ = 128
Answer: x⁷
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Start practisingCommon mistake. Pupils often multiply the indices instead of adding them when multiplying powers, turning a³ × a² into a⁶ rather than the correct a⁵, confusing the multiplication law with the power-of-a-power law.
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