Properties of Exponents.

For a large group of students doing arithmetic operations on monomials and polynomials is a challenging and scary task to take on. All those little rules... should I add the exponents? Should I multiply the exponents? Should I subtract the exponents? ...How do I simplify this expression with all those little numbers in the upper right of the variables?

You may very well start forgetting to ask all those questions; after you study this lesson you will be able to effectively apply them to simplify any expression that may require them. You will know exactly when to apply the Product of a Power, or the Power of a Power, or any other of them. Nevertheless, important to say: Good if you go through the vocabulary given below the lesson's box inside the webpage. Many of them might be too formal or include many unknown words. But together with the lesson itself will be very helpful. Through the lesson you might go back to re-read some of them. Try it! Now a good student will benefit from highlighting parts of the solution, or writing notes along the lesson. You may accomplish this using the MARKER TOOLS menu provided at the upper right section of the lesson's box.

Lesson's Content

Lesson In PDF Format (no animations)


Lesson's Glossary

Algebraic expression: A given set of letters called variables, and real numbers called constants that are combined using addition, subtraction, multiplication, division and/or exponentiation. 

Constant: It is a number or value that remains always the same. Never changes.

Exponent: It is a raised number representing the repeated multiplication of a given factor.

Perfect square trinomial: A trinomial generated by the product of two equal binomials.

Expression: Any combination of numbers and operations without the = sign. 

Factors: All whole numbers that are multiplied together to yield another number.

Like terms: Terms that have the same combination of variables to the same power as factors.

Operation: Any action we perform on one or two numbers to produce a new number. Most common ones are addition, subtraction, multiplication, division, square roots, powers, and so on.

Polynomial: A algebraic statement with one or more terms. Word comes from “poly” which means many.

Power: Exponent of a number or variable.

Subtraction: Adding the opposite.

Term: A form of grouping one or more numerical and/or variable factors by means of multiplication and division. Addition and subtraction symbols separate terms.

Variable: A letter used to represent a number. When the variable is part of an equation, it is possible to find the value for which it stands for by solving the equation. This is the solution (s) of the equation.

Variable expression: Mathematical phrase with at least one variable in it.


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