Basic Algebra/Polynomials/Exponents
Vocabulary
editBase: 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
editExponents 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
editPractice Games
editPractice Problems
editUse ^
for exponentiation and remember Order of Operations