Powers and Number Operations

Name:

Date:

🎯 Part 1: Quick Check for Understanding

1. Write 3,450 in expanded form using powers of 10.

2. What is 10⁻³ as a fraction and as a decimal?

Fraction: _________ Decimal: _________

3. Calculate 5³ and find ∛125.

5³ = _________ ∛125 = _________

4. Write these numbers in order from smallest to largest: 10², 10⁻¹, 10⁰

5. Express 72 as a product of prime factors using exponents.

6. Use the radical symbol to represent the square root of 49 and the cube root of 64.

Square root of 49: _________ Cube root of 64: _________

7. A scientist measures bacteria growth. Day 1: 10² bacteria, Day 2: 10⁴ bacteria. How many times larger is Day 2 than Day 1?

8. Convert 0.001 to a negative power of 10, then write it in expanded form.

9. Find √81 and ∛27. Use a calculator to approximate √50 to 2 decimal places.

√81 = _____ ∛27 = _____ √50 ≈ _____

10. Write 2.34 × 10³ in standard form, then in expanded form using powers of 10.

11. Find the prime factorisation of 48 and write it using exponents.

12. Explain why 10⁰ = 1. Use an example to support your reasoning.

13. Challenge: If 2ⁿ = 64, what is the value of n? Show your working.