In order to successfully perform operations with polynomials, one must have a complete understanding of the rules of exponents. We will review: the product rule for exponents, the quotient rule for exponents, the power rules for exponents, negative exponents, and the power of zero.

Test Objectives
• Demonstrate an understanding of the product/quotient rule for exponents
• Demonstrate an understanding of the power rules for exponents
• Demonstrate an understanding of negative exponents and the power of zero
Exponent Rules Practice Test:

#1:

Instructions: Simplify each.

a) $$\frac{2hj^0k^{-7} \cdot -h^0j^{-1}k^4}{(2k^2)^8}$$

#2:

Instructions: Simplify each.

a) $$\frac{-x^0y^3z^7\cdot(-y^2z^8)^5}{-2x^5y^3z^0}$$

#3:

Instructions: Simplify each.

a) $$-\frac{2ba^{-6}c^8}{(2a^8b^0c^{-7}\cdot 2a^3c^{-5})^5}$$

#4:

Instructions: Simplify each.

a) $$\frac{(-q^8r^6)^4}{(-p^2q^2r^5q\cdot p^3r^0)^0}$$

#5:

Instructions: Simplify each.

a) $$\frac{(2bca^{-1})^3}{-2b^2c^2\cdot-a^7b^{-3}}$$

Written Solutions:

#1:

Solutions:

a) $$\frac{-h}{2^7k^{19}j}$$

#2:

Solutions:

a) $$\frac{-y^{10}z^{47}}{2x^5}$$

#3:

Solutions:

a) $$-\frac{bc^{68}}{2^9a^{61}}$$

#4:

Solutions:

a) $$q^{32}r^{24}$$

#5:

Solutions:

a) $$\frac{4b^4c}{a^{10}}$$