This study notes covers Worked Example 3: Negative Bases within Powers & Roots for GCSE Mathematics. Revise Powers & Roots in Number for GCSE Mathematics with 15 exam-style questions and 22 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 9 of 14 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Worked Example 3: Negative Bases
Calculate: (a) (-3)² (b) -3²
Solution
(a) (-3)² = (-3) × (-3) = 9
The brackets mean square the negative number
(b) -3² = -(3 × 3) = -9
No brackets means square 3, then make negative
Brackets make all the difference!
Practice questions for Powers & Roots
What is the value of 2⁻³?
Explain why x⁻¹ = 1/x
Quick recall flashcards
Powers of 10
10¹ = 10
10² = 100
10³ = 1,000
10⁴ = 10,000
10⁵ = 100,000
10⁶ = 1,000,000
Pattern: n zeros after 1
Cubes: 1³ to 5³
1³ = 1
2³ = 8
3³ = 27
4³ = 64
5³ = 125