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 = 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]

Practice Problems
Use  for exponentiation and remember Order of Operations  { x3 × x6 = { x^9 (i) _15 }
 * type="{}"}

{ ax × a3 = { a^(x + 3) (i)|a^(x+3) (i) _15 }
 * type="{}"}

{ x4 / x2 = { x^2 (i) _15 }
 * type="{}"}

{ (a4b)3 = { a^12 * b^3 (i)|a^12*b^3 (i)|a^12b^3 (i) _15 }
 * type="{}"}

{ (a2b3c)3 = { a^6 * b^9 * c^3 (i)|a^6*b^9*c^3 (i)|a^6b^9c^3 (i) _15 }
 * type="{}"}