Exponential Functions
Linera Equations
Simple Trinomials as Products of Binomials
Laws of Exponents and Dividing Monomials
Solving Equations
Multiplying Polynomials
Multiplying and Dividing Rational Expressions
Solving Systems of Linear Inequalities
Mixed-Number Notation
Linear Equations and Inequalities in One Variable
The Quadratic Formula
Fractions and Decimals
Graphing Logarithmic Functions
Multiplication by 111
Solving Systems of Equations - Two Lines
Solving Nonlinear Equations by Factoring
Solving Linear Systems of Equations by Elimination
Rationalizing the Denominator
Simplifying Complex Fractions
Factoring Trinomials
Linear Relations and Functions
Axis of Symmetry and Vertices
Equations Quadratic in Form
The Appearance of a Polynomial Equation
Subtracting Reverses
Non-Linear Equations
Exponents and Order of Operations
Factoring Trinomials by Grouping
Factoring Trinomials of the Type ax 2 + bx + c
The Distance Formula
Invariants Under Rotation
Multiplying and Dividing Monomials
Solving a System of Three Linear Equations by Elimination
Multiplication by 25
Powers of i
Solving Quadratic and Polynomial Equations
Slope-intercept Form for the Equation of a Line
Equations of Lines
Square Roots
Integral Exponents
Product Rule for Radicals
Solving Compound Linear Inequalities
Axis of Symmetry and Vertices
Multiplying Rational Expressions
Reducing Rational Expressions
Properties of Negative Exponents
Numbers, Factors, and Reducing Fractions to Lowest Terms
Solving Quadratic Equations
Factoring Completely General Quadratic Trinomials
Solving a Formula for a Given Variable
Factoring Polynomials
Decimal Numbers and Fractions
Multiplication Properties of Exponents
Multiplying Fractions
Multiplication by 50

Try the Free Math Solver or Scroll down to Tutorials!












Please use this form if you would like
to have this math solver on your website,
free of charge.

1. Exponents:

An exponent is a number that indicates how many times the base is to be used as a factor. Exponents indicate repeated multiplication.

The base is the number that is multiplied.

Ex: Identify the base and the exponent: 2 3

Two is the base and three is the exponent.


2. Zero exponent:

Any number other than 0 raised to the zero power is 1.


3. Order of operations:

When evaluating mathematical expressions, we will perform operations in the following order:

First: If the expression contains grouping symbols, such as parenthesis (), brackets [ ], braces { }, or a fraction bar, then we perform the operations inside the grouping symbols, or above and below the fraction bar, first.

Second: Evaluate, or simplify, any numbers with exponents.

Third: Do all multiplications and divisions in order from left to right.

Fourth: Do all additions and subtractions in order from left to right.

Ex: Simplify. 2 + 3•5

2 + 3•5   (operations of addition and multiplication are present)
   = 2 + 15 (perform multiplication first)
   = 17 (perform addition second)


 b. 3 + 2•42

3 + 2•42   (operations of addition, mult, and exponentiation)
   = 3 + 2•16 (do exponents first)
   = 3 + 32 (do multplication second)
   = 35 (do addition third)


4. Vocabulary:

We will now translate into mathematical symbols English phrases that contain complicated expressions involving the terms sum, product, difference, and quotient.

English phrase Math symbols
sum of a and b a + b
two times the sum of a and b 2(a + b)
product of p and q p · q
product of p and the sum of a and b p · (a + b)
sum of p and the product of a and b p + a · b
difference of p and the sum of a and b p - (a + b)
sum of the product of a and b and the product of c and d a · b + c · d

Ex: Translate each phrase into math symbols.

a. product of 4 and the sum of 3 and x

Answer: 4 · (3 + x)

b. difference of 4 and the sum of 3 and x

Answer: 4 - (3 + x)

c. sum of the product of 4 and 3 and the product of 2 and 5

Answer: 4 · 3 + 2 · 5

d. twice the product of 4 and x

Answer: 2 · (4 · x)

e. twice the sum of 8 and 5

2 · (8 + 5)