Learn the fundamental laws of indices for multiplying and dividing powers with the same base
The laws of indices allow us to simplify expressions involving powers. These fundamental rules make working with large numbers and algebra much more efficient.
Index laws are essential for working with very large and very small numbers in science and engineering.
These laws form the foundation for simplifying algebraic expressions and solving equations in GCSE and A-level maths.
Understanding index laws allows you to perform calculations more quickly and accurately.
Question: Simplify 25 × 23
Solution: Same base (2), so add the indices:
25 × 23 = 25+3 = 28
Answer: 28 = 256
Question: Simplify 57 ÷ 54
Solution: Same base (5), so subtract the indices:
57 ÷ 54 = 57-4 = 53
Answer: 53 = 125
Question: Simplify x4 × x6
Solution: Same base (x), add the indices:
x4 × x6 = x4+6 = x10
Answer: x10
Question: Simplify y9 ÷ y2
Solution: Same base (y), subtract the indices:
y9 ÷ y2 = y9-2 = y7
Answer: y7
Learn from typical errors students make and discover how to avoid them!
What students often do wrong:
Students often multiply the indices instead of adding them. For example, they calculate 23 × 24 = 212 instead of 27. They also sometimes change the base incorrectly.
Correct approach: Remember: multiply powers → ADD indices. The base NEVER changes. 23 × 24 = 23+4 = 27
Memory tip: "Multiply the terms, ADD the powers"
Write out what the indices mean: 23 × 24 = (2×2×2) × (2×2×2×2) = 27. This helps you see why you add the indices.
You've mastered the laws of indices for multiplication and division!
Next: Explore square numbers, square roots, and perfect squares