Basic Algebra/Polynomials/Exponents

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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


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]

Practice Games[edit]

Practice Problems[edit]

Use ^ for exponentiation and remember Order of Operations


x3 × x6 =


ax × a3 =


x4 / x2 =


(a4b)3 =


(a2b3c)3 =