📚 Part 1: Basic Exponents - Answer Key

Answer: 8

Working: 2³ = 2 × 2 × 2 = 8

Answer: 25

Working: 5² = 5 × 5 = 25

Answer: 64

Working: 4³ = 4 × 4 × 4 = 64

Answer: 7

Note: The base is the number being multiplied by itself

Answer: 5

Note: The exponent tells us how many times to multiply the base by itself

✏️ Part 2: Exponent Rules - Answer Key

Answer: 3⁵ = 243

Working: When multiplying powers with the same base, add the exponents: 3² × 3³ = 3²⁺³ = 3⁵

Calculation: 3⁵ = 3 × 3 × 3 × 3 × 3 = 243

Answer: 5⁴ = 625

Working: When dividing powers with the same base, subtract the exponents: 5⁶ ÷ 5² = 5⁶⁻² = 5⁴

Calculation: 5⁴ = 5 × 5 × 5 × 5 = 625

Answer: 2⁶ = 64

Working: When raising a power to a power, multiply the exponents: (2³)² = 2³ˣ² = 2⁶

Calculation: 2⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64

🌟 Part 3: Extension Questions - Answer Key

Answer: x = 4

Step-by-step solution:

• We need to find what power of 2 equals 16

• Let's work through powers of 2:

• 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16

• Therefore, x = 4

Answer: 48 bacteria

Step-by-step solution:

• Initial amount: 3 bacteria

• After each hour, the population doubles (multiplies by 2)

• After 4 hours: 3 × 2⁴ = 3 × 16 = 48 bacteria

• Alternative working: Hour 1: 6, Hour 2: 12, Hour 3: 24, Hour 4: 48

Sample Answer:

Any number to the power of 0 equals 1 because of the division rule for exponents. For example:

• 5³ ÷ 5³ = 5³⁻³ = 5⁰

• But 5³ ÷ 5³ = 125 ÷ 125 = 1

• Therefore, 5⁰ = 1

Note for teachers: Accept any clear explanation that demonstrates understanding of this concept

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