Handout for Sections P.2, P.3, 2.3, and 1.7
College Algebra
Exponents:
Radicals:
Product Rule: 𝑏 𝑚 ∙ 𝑏 𝑛 = 𝑏 𝑚+𝑛
√𝑎2 = |𝑎|
Quotient Rule:
𝑏𝑚
𝑏𝑛
𝑛
If n is odd, √𝑎𝑛 = 𝑎
= 𝑏 𝑚−𝑛
𝑛
If n is even, √𝑎𝑛 = |𝑎|
Zero Exponent Rule: 𝑏 0 = 1, 𝑏 ≠ 0
𝑛
𝑛
1
𝑛
Negative Exponent Rule: 𝑏 −𝑛 = 𝑏𝑛 , 𝑏 ≠ 0
Product Rule: √𝑎 ∙ √𝑏 = √𝑎𝑏
Power Rule: (𝑏 𝑚 )𝑛 = 𝑏 𝑚𝑛
Quotient Rule: √ 𝑏 =
𝑛
(𝑎𝑏)𝑛 = 𝑎𝑛 𝑏 𝑛
𝑎
𝑛
𝑛
√𝑎
𝑛
√𝑏
𝑛
√𝑎 = 𝑎1/𝑛
𝑎𝑛
( 𝑏 ) = 𝑏𝑛
𝑛
𝑛
√𝑎 𝑚 = ( √𝑎 )
1
𝑛
√𝑎
𝑛
𝑅𝑖𝑠𝑒
𝑅𝑢𝑛
𝑦 −𝑦
= 𝑥2 −𝑥1
2
Types of Linear Equations:
Point-Slope Form: 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 )
Slope-Intercept Form: 𝑦 = 𝑚𝑥 + 𝑏
General Form: 𝐴𝑥 + 𝐵𝑦 + 𝐶 = 0
1
𝑚
= 𝑎𝑚/𝑛
= 𝑎 −1/𝑛 , 𝑎 ≠ 0
1
√𝑎𝑚
Slope of a linear equation: 𝑚 =
𝑎
=
1
𝑛
( √𝑎 )
𝑚
1
= 𝑎𝑚/𝑛 = 𝑎−𝑚/𝑛