AlgebraLab

Algebra I Recipe: Exponents and Order of Operations

By G Redden

A. Definitions
  1. base – any number, variable, or term raised to an exponent.
  2. exponent – it tells how many times to multiply the base by itself.
    • Given 73, 7 is the base, 3 is the exponent, and it means 7 · 7 · 7.
    • Given x5, x is the base, 5 is the exponent, and it means x · x · x · x · x.
    • Given (2x)4, 2x is the base, 4 is the exponent, and it means 2x · 2x · 2x · 2x.
    • Given 2x4, x is the base, 4 is the exponent, and it means 2 · x · x · x · x.
    • Therefore, (2x)4 and 2x4 would not have the same value.
B. Order of Operations
  1. Do all operations within grouping symbols.
  2. Evaluate exponents.
  3. Do multiplication and division from left to right.
  4. Do addition and subtraction from left to right.
1.
Evaluate x3 when x = 5.
2.
Evaluate (3a + 6b)2 when a = 1 and b = 2.
3.
Evaluate 2x3 when x = 4.
4.
Evaluate (2x)3 when x = 4.
C. Formulas of a Cube

  1. Surface Area – the space that covers all sides of the cube where each side or face is exactly the same.
    • Find the area of one side or face.
    • Multiply that area by 6 since there are 6 identical sides or faces.
    • Answer must be in square units such as in2, ft2, cm2.
  2. Volume – the space inside the cube.
    • Multiply the length, width, and height of the cube together. V = l · w · h
    • Answer must be in cubic units such as in3, ft3, or cm3
Companion Exercises Practice Problems