GCSE Maths | Indices

Power of 2

• 1² = 1
• 2² = 4
• 3² = 9
• 4² = 16
• 5² = 25
• 6² = 36
• 7² = 49
• 8² = 64
• 9² = 81
• 10² = 100
• 11² = 121
• 12² = 144

Power of 3

• 1³ = 1
• 2³ = 2 x 2 x 2 = 8
• 3³ = 3 x 3 x 3 = 27
• 4³ = 64
• 5³ = 125
• 10³ = 1000

Power of 4

• 1⁴ = 1
• 2⁴ = 2 x 2 x 2 x 2 = 16
• 3⁴ = 3 x 3 x 3 x 3 = 81

Rule 1

• x³ x x⁵ = x⁸
• x⁵/x³ = x²

Question 1

Rule 2

• (x³)² = x⁶

Question 2

Question 3

Rule 3

• (4/5)^-1 = 5/4

Question 4

Rule 4

• 16^1/2 = 4 (square root)
• 8^1/3 = 2 (cube root)

Question 5

Combining Powers and Roots

• 9^3/2 means square root 9 then cube it
• 8^2/3 means cube root 8 then square it

Question 6

Question 7