Laws of Exponents

Name: ____________________

Date: _____________________

Simplify each expression below using the laws of exponents. Show your work where necessary.

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 (Multiplying)

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

Part 2: Quotient Rule (Dividing)

5. $\frac{b^{12}}{b^5} = $
6. $\frac{y^8}{y^7} = $
7. $\frac{15c^9}{3c^4} = $
8. $\frac{24d^5e^3}{8d^2e^2} = $

Part 3: Power Rule (Power to a Power)

9. $(p^4)^6 = $
10. $(k^3)^2 = $
11. $(2w^5)^3 = $
12. $(4x^2y^3)^2 = $

Part 4: Mixed Practice

13. $(x^4)(x^5) = $
14. $\frac{18m^{10}}{3m^2} = $
15. $(y^7)^3 = $
16. $(5a^2b^4)(2a^3b) = $
17. $\frac{g^9}{g^3} = $
18. $(3z^4)^4 = $