Worksheet Chapter 1: Indices

1. True or False: Any non-zero number raised to the index of 0 is always equal to 0.

2. Which of the following expressions is equivalent to (3a²b³) × (4ab²)?

3. Simplify (16x⁸y⁻⁴)¹/4) and write the answer with positive indices only.

4. Fill in the blank: In the expression 7⁵, the number 7 is called the _______ and 5 is called the _______.

5. Solve the equation: 3ˣ × 9^(x - 1) = 27.

6. State whether (x⁻⁴) is equal to (-x⁴). Select True if equal, or False if not equal.

7. Evaluate the exact numerical value of 64²/3) without using a calculator.

8. Given that 2ˣ = p and 2ʸ = q, express 8^(x + y)4ʸ in terms of p and q.

9. Solve the exponential equation: 4^(x + 1) = 64.

10. Simplify the expression (m⁵ × m⁻²) ÷ m³ and express your answer in index form.