Exponents — Important Questions

2 × 5^4

Step 1: Perform prime factorisation of 1250. Step 2: 1250 ÷ 2 = 625. Step 3: 625 = 5 × 5 × 5 × 5 = 5^4. Step 4: So 1250 = 2 × 5^4. Verify: 2 × 625 = 1250. ✓ Common mistake: Stopping factorisation early or grouping factors incorrectly.

72

Step 1: Evaluate 4^2 = 16 and 2^3 = 8 and 3^2 = 9. Step 2: Solve the bracket first: 4^2 - 2^3 = 16 - 8 = 8. Step 3: Multiply the bracket result by 3^2: 8 × 9 = 72. Common mistake: Not following BODMAS — students sometimes multiply before solving the bracket.

17

Step 1: Substitute a = 3, b = 2 into a^b + b^a. Step 2: a^b = 3^2 = 3 × 3 = 9. Step 3: b^a = 2^3 = 2 × 2 × 2 = 8. Step 4: Add both values: 9 + 8 = 17. Common mistake: Confusing a^b with b^a — note that 3^2 ≠ 2^3.

2^8, because 256 > 64

Step 1: Calculate 2^8 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256. Step 2: Calculate 8^2 = 8 × 8 = 64. Step 3: Compare: 256 > 64. Step 4: Therefore 2^8 > 8^2. Lesson: A larger base does not always give a larger result — the exponent also matters greatly.