Basic Algebra/Polynomials/Exponents

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Vocabulary[edit]

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[edit]

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 = a3 + 2 = a5

3) When we divide the same base we subtract our exponents: a6 / a4 = a6 - 4 a2

4) When we raise a power to a power we multiply our exponents: (a2)3 = a2 * 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]

Example Problems[edit]

x3 * x6 = ?? [= x9]

ax * a3 = ?? [= ax + 3]

x4 / x2 = ?? [= x2]

(a4b)3 = ?? [= a12b3]

(a2b3c)3 = ?? [= a6b9c3]

Practice Games[edit]

Practice Problems[edit]