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Exponent Laws Mastery

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Exponent Laws Mastery worksheet preview

Exponent Laws Mastery

Mathematical exponents illustration

📚 Part 1: Simplifying Numerical Expressions

1. Simplify the following expressions:

a) 5-3 = __________

b) 25 ÷ 23 = __________

c) 70 = __________

d) 4-2 = __________

e) 34 ÷ 36 = __________

2. Evaluate these expressions:

a) (2 × 3)2 = __________

b) 10-1 = __________

c) 63 ÷ 63 = __________

3. Which of the following equals 1/8?

2-3

8-1

23

Both a) and b)

✏️ Part 2: Algebraic Expressions with Variables

4. Simplify these algebraic expressions:

a) (3x)2 = __________

b) y0 = __________

c) a3 ÷ a5 = __________

d) x4 × x-2 = __________

e) (m2)3 = __________

5. Apply the index laws to simplify:

a) b6 × b-4 = __________

b) (2p)3 = __________

c) n5 ÷ n8 = __________

6. True or False? Circle your answers:

a) Any number to the power of 0 equals 1 True / False

b) x-3 = -x3 True / False

c) a2 × a3 = a5 True / False

🤔 Part 3: Understanding and Explanation

7. Explain in your own words what a zero exponent means. Use an example in your explanation.
8. Explain what a negative exponent means. Show why 3-2 = 1/9 using the pattern of exponents.
9. Challenge Problem: Simplify completely and show your working:

(2a3b)2 ÷ (a2b-1)

10. Partner Discussion: Discuss with your partner why the index laws work the same way for both numbers and variables. Write one key insight below:

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