Simplifying Expressions with Multiple Index Laws

Name: ___________________________
Date: ___________________________

Index Laws Reminder:

• am × an = am+n
• am ÷ an = am-n
• (am)n = amn
• a0 = 1

Part A: Simplify these expressions

1. x5 × x3 ÷ x2 = _____________________
2. (y4)2 × y3 = _____________________
3. a8 ÷ a3 ÷ a2 = _____________________
4. (m3)4 ÷ m7 = _____________________
5. p6 × (p2)3 = _____________________
6. b10 ÷ (b2)3 = _____________________

Part B: Simplify these more complex expressions

7. (x3)2 × x4 ÷ x5 = _____________________
8. t9 ÷ (t2)3 × t4 = _____________________
9. (k5 × k3)2 = _____________________
10. (n8 ÷ n2)3 = _____________________
11. c12 ÷ (c3)2 ÷ c3 = _____________________
12. (z4)3 × z5 ÷ (z2)4 = _____________________

Part C: Challenge questions

13. (a3 × a5)2 ÷ (a4)3 = _____________________
14. r15 ÷ (r3 × r2)2 = _____________________
15. (d6 ÷ d2)3 × d4 ÷ d10 = _____________________