College Algebra - Simplifying Polynomials - Properties of Exponents

Simplifying Polynomials-Properties of exponents

Properties of exponents
𝑎 𝑏 𝑎+𝑏
Product Rule of Exponents: 𝑥 𝑥 =𝑥
When multiplying the same variables, simply add their exponents.
3 3 4 2 3+4 3+2 7 5
Example; (2𝑥 𝑦 )(3𝑥 𝑦 ) = 6𝑥 𝑦 = 6𝑥 𝑦


𝑎
𝑥 𝑎−𝑏
Quotient Rule of Exponents: 𝑏 =𝑥
𝑥
When dividing the same variable, subtract their exponents.
𝑎
𝑥 1
If a<b, the exponent is negative , or 𝑏 = 𝑏−𝑎
𝑥 𝑥
3 4 4−2 2
4𝑥 𝑦 3−5 4−2 −2 2 2𝑦 2𝑦
Example; 5 2 = 2𝑥 𝑦 = 2𝑥 𝑦 𝑜𝑟 5−3 = 2
2𝑥 𝑦 𝑥 𝑥



𝑎 𝑏 𝑎𝑏
Power of a Power Rule of Exponents: (𝑥 ) = 𝑥
When a variable is raised to another exponential power, multiply the exponents.
3 2 3(2) 6
example; (4𝑥 ) = 16𝑥 = 16𝑥


𝑎 𝑎 𝑎
Power of a Product Rule of Exponents: (𝑥𝑦) = 𝑥 𝑦
When the product of two variables is raised to exponential power, distribute the
exponent.

5 5 5
Example; (3𝑥𝑦) = 243𝑥 𝑦



𝑥 𝑎
𝑎
𝑥
Power of a Quotient Rule of Exponents: ( ) = 𝑎
𝑦 𝑦
When the quotient of two variables is raised to exponential power, distribute the
exponent.
𝑥 3
3
𝑥
Example; ( 2𝑦
) = 3
8𝑦