Basic Algebra/Polynomials/Exponents

Vocabulary

Base: The number directly preceding an exponent

EX: a² -> a is the base

Exponent: The number (written in superscript) used to express how many times a base is multiplied by itself

EX: a⁴ = a * a * a * a -> 4 is the exponent

EX: 4³ = 4 * 4 * 4 = 64 -> 3 is the exponent

Lesson

Exponents are a simple way to represent repeated multiplication. For example a x a = a². There are a few simple rules for exponents that help reduce very large problems to simple little ones. The rules are as follows:

1) The exponent of any number is always a one (1): a = a¹

2) When we multiply the same base we add our exponenents: a³ x a² = a^{3 + 2} = a⁵

3) When we divide the same base we subtract our exponents: a⁶ / a⁴ = a^{6 - 4} = a²

4) When we raise a power to a power we multiply our exponents: (a²)³ = a^{2 * 3} = a⁶

5) When we raise a PRODUCT to a power we raise both parts of the product to the power: (ab)³ = a³b³ [NOTE: This ONLY works with multiplication and NOT addition: (a + b)³ ≠ a³ + b³]

6) When we raise a QUOTIENT to a power we raise both parts of the quotient to the power: (a/b)² = a² / b² [NOTE: This ONLY works with division and NOT subtraction: (a - b)² ≠ a² - b²]

Practice Problems

Use ^ for exponentiation and remember Order of Operations

1

x3 × x6 =

2

ax × a3 =

3

x4 / x2 =

4

(a4b)3 =

5

(a2b3c)3 =