Laws of Exponents: Practice

Name: ____________________

Date: _____________________

Simplify each expression below using the laws of exponents.

Exponent Rules Review

Product Rule: $x^a \cdot x^b = x^{a+b}$
Quotient Rule: $\frac{x^a}{x^b} = x^{a-b}$
Power Rule: $(x^a)^b = x^{a \cdot b}$

Part 1: Product Rule

1. $y^7 \cdot y^2 = $
2. $b^4 \cdot b^6 = $
3. $(3x^5)(4x^3) = $
4. $(-2a^2b^3)(5ab^4) = $
5. $(m^3n^2)(m^8n^5) = $
6. $(-x^4y)(-7x^2y^6) = $

Part 2: Quotient Rule

7. $\frac{z^{10}}{z^3} = $
8. $\frac{x^5}{x} = $
9. $\frac{20a^8}{5a^2} = $
10. $\frac{18x^6y^4}{6x^3y} = $
11. $\frac{32m^{12}n^5}{4m^8n} = $
12. $\frac{p^{15}}{p^4} = $

Part 3: Power Rule

13. $(x^5)^3 = $
14. $(y^8)^2 = $
15. $(3a^2)^4 = $
16. $(5m^3n^2)^3 = $
17. $(-4k^3)^2 = $
18. $(c^2d^7)^3 = $

Part 4: Mixed Practice

19. $(x^2)^5 \cdot x^3 = $
20. $\frac{(y^4)^3}{y^6} = $
21. $(-3p^4q)^2 = $
22. $(2a^3b)^3 \cdot a^2b = $
23. $(5x^4y)(2x^2y^3) = $
24. $\frac{24a^7b^3}{8a^2b^2} = $
25. $\frac{(2x^2)^3}{x^4} = $
26. $(a^5b^2)^2 \cdot (ab)^3 = $