Index Laws Practice

Name:

Date:

📚 Part 1: Multiple Choice & Matching

Learning intentions: Recall and apply index laws, including negative and fractional indices.

Success criteria: I can simplify expressions using index laws and explain one rule in my own words.

Differentiation / dyslexia-friendly options: Use coloured pens to mark bases and exponents; calculators may be used to check fractional or negative powers. Sentence starters: “I subtract exponents because…”, “I raise the power to a power by…”

1. Simplify: m⁴ × m^-1

m³

m⁵

m^-3

2. Simplify: x^3/2 ÷ x^1/2

x^1/2

x²

x^3/4

3. Simplify: (2a²b^-3)³

8 a⁶ b^-9

6 a⁵ b^-6

8 a⁵ b^-9

8 a⁶ b⁹

4. Evaluate: 5⁰ + 3^-2

10/9

1.111…

9/10

5. Match the index law name (left) with its formula (right).

A. Product law

B. Quotient law

C. Zero power law

D. Power of a power

E. Power of a product

F. Power of a quotient

1. (a/b)^m = a^m / b^m

2. a^m × aⁿ = a^m+n

3. a⁰ = 1 (a ≠ 0)

4. (ab)^m = a^m b^m

5. a^m / aⁿ = a^m−n

6. (a^m)ⁿ = a^mn

✏️ Part 2: Short Answers

6. Simplify and show working: (c^-2)³

7. Simplify: b^3/2 ÷ b^1/2 (show steps)

8. Simplify and simplify powers of negatives/fractions: ( (3 x^1/3) / y^-2 )²

9. Explain in one sentence why a⁰ = 1 for a ≠ 0.

10. Extension (challenge): Simplify fully: (x^3/2 y^-1) ÷ (x^1/2 y²)

Extension activities: Try problems with mixed fractional indices or apply index laws to scientific notation. For advanced learners: prove the zero power rule using the quotient law and examples.

Teacher notes: Encourage use of calculators to check fractional and negative powers; prompt students to state which index law they used each step.