📚 Part 1: Laws of Indices

1. Simplify the following expressions using the laws of indices:

a) 3² × 3³ = _______

b) (x³)⁴ = _______

c) y⁵ ÷ y² = _______

2. What does a^(1/2) represent?

Half of a

The square root of a

a divided by 2

2 multiplied by a

3. Calculate the following fractional powers:

a) 9^(1/2) = _______

b) 8^(1/3) = _______

c) 16^(3/4) = _______

4. Simplify these expressions with negative and fractional indices:

a) 4^(-1/2) = _______

b) (x³y⁻¹)² = _______

✏️ Part 2: Solving Fractional Equations

5. Solve the following equations involving fractional powers:

a) x^(2/3) = 16

x = _______

b) x^(1/2) = 5

x = _______

6. Solve these equations with fractional coefficients:

a) (2/3)x - 4 = 1/3

x = _______

b) (1/2)x^(1/2) = 3

x = _______

7. Which of the following are equivalent to 27^(2/3)?

(∛27)²

9

(27²)^(1/3)

18

🎯 Part 3: Challenge Questions

8. Simplify completely: (8x⁶)^(2/3) ÷ (2x²)^(1/3)

Answer: _________________

9. Solve: (x + 1)^(3/2) = 8

x = _______

10. Explain in your own words why fractional powers are useful in mathematics:

Powers and Fractional Equations

Powers and Fractional Equations

📚 Part 1: Laws of Indices

✏️ Part 2: Solving Fractional Equations

🎯 Part 3: Challenge Questions

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