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The Power of Powers
The Power of Powers
When you calculate the area of a square room that's 5m × 5m, you write 5² = 25m². When finding the volume of a cube box that's 3m × 3m × 3m, you write 3³ = 27m³. Powers (indices) are a shorthand for repeated multiplication, while roots help us work backwards - if a square has area 64m², its side length is √64 = 8m.
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Common Mistakes to Avoid
❌ Wrong: 2³ = 6
✅ Right: 2³ = 8
Powers mean multiply, not add: 2×2×2 not 2×3
❌ Wrong: √9 = ±3
✅ Right: √9 = 3
Square root symbol means positive root only
❌ Wrong: (-2)² = -4
✅ Right: (-2)² = 4
Negative × negative = positive
❌ Wrong: -4² = 16
✅ Right: -4² = -16
Without brackets: square first, then apply negative
Now try it yourself
Quiz · Question 1 of 15
What is the value of 2⁻³?
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This topic in real past papers
Every real exam question we've found on powers & roots, with a full worked answer.