Variables with Exponents

 You’ve heard about mathematicians, right? They’re always in trouble because they worship the sum, tee hee. This might be true! They certainly have lots of problems. Some of a mathematician’s problems concern all the variables he has to deal with, for they aren’t what they seem. You see, a variable is a letter that stands for a number. Problems, which are also called expressions (creative, huh?) with variables often come with exponents, those itsy bitsy little numbers that are placed up high and to the right of the variable. They tell you the power to raise the variable or, in other words, how many times the constant or variable must be multiplied by itself. Variables with exponents are rather like a code one has to solve to learn an expression’s true meaning.

You can do virtually everything with a variable that you can do with a number. Soon, you’ll be adding variables with exponents, multiplying variables with exponents, dividing variables with exponents, and more. Most of the time the problem provides the value for one or more of the variables. Later, when you learn how to simplify radicals with variables and exponents, you’ll be able to move on to rationalizing the denominators and numerators that found in radical expressions.

When working with expressions that include exponents with variables, it is important to keep the order of operations in mind. Many people simply use the mnemonic, “Please Excuse My Dear Aunt Sally” to help them remember the order to perform operations. The first letter of each word gives you your memory clue: parentheses, exponents, multiplication/division and addition/subtraction.

Each expression you work will bring you new challenges, but by being methodical and sticking to the basics, you’ll not have any trouble.

If a problem provides a known number for one of the variables, start by substituting those numbers for the appropriate variables. So, for example, if your problems were like this one:

-3 x5 – 4y = -2 where y = 2x – 5

The first thing you would do is to substitute put 2x – 5 for y in the problem, making it look like this:

-3 x5 – 4 = 4(2x – 5) = -2

And then solve for x.

To add variables with exponents, such as this problem, one that also contains constants, necessitates:

(3 x2 y2) (4 x2)

First multiply the constants, then the variables, and then add the variables. The work on this problem would look like this:

3∙4 x 2+2 y2 = 12 x 4 y2

While you might wish to familiarize yourself with an exponent calculator with variables, it’s unnecessary in this example, where one simply adds the exponents.

For exponent multiplying exponents with variables, just remember that the exponent tells you how many times the variable is multiplied by itself. So,

y6y6 really means (yyyyyy) (yyyyyy) = y12

It’s quite simple if you memorize the laws and practice until you understand the concept well. Just remember, be careful not to miss too many math classes, because if you do, it’s going to add up in a negative way.