## How to simplify expressions with variables and exponents Simplifying Exponent Expressions

Use the product to a power property of exponents to simplify expressions You have seen that when you combine like terms by adding and subtracting, you need to have the same base with the same exponent. But when you multiply and divide, the exponents may be different, and sometimes the bases may be different, too. Simplify the following expression: 6 8 6 5. \mathbf {\color {green} {\dfrac {6^8} {6^5}}} The exponent rules tell me to subtract the exponents. But let's suppose that I've forgotten the rules again. The " 68 " means I have eight copies of 6 on top; the " 65 " means I have five copies of 6 underneath.

Which mostly showed examples of how to deal with simplifying and calculating with numbers and their exponents. Mathematical expressions and equations can also include variables with exponents, and these expressions can also be simplified and manipulated at times.

When manipulating expressions in Algebra, something that is handy to know is the difference and sum of two cubes, along with a similar rule for squares. When learning to solve equations in Algebra, literal equations examples will eventually appear. Find out more about how to solve them here. As well as one step equations, there are also multi step equations examples which can be encountered in Algebra.

Examples 1. This can be simplified by expfessions considering each term separately. This expression can be simplified by looking at what's inside the brackets, and looking at eponents effect the exponent outside the brackets has.

We can attempt simplifying expressions with exponents like this by thinking how to trim persian cat hair what each term on the top and bottom of the fraction represent.

Can again simplify by using the same thought process. Solution A good first step in simplifying expressions with exponents such as this, is to look to group like terms together, then proceed. Solution Similar to before, look to group into separate fractions containing like terms. Recent Articles.

Simplifying Variable Expressions Using Exponent Properties I

This leads to another rule for exponents—the Power Rule for Exponents. To simplify a power of a power, you multiply the exponents, keeping the base the same. For example, (23)5 = (2 3) 5 = 2 This leads to the Power Property for Exponents. zi255.com offers valuable advice on simplify expressions with exponents and multiple variables, syllabus for elementary algebra and complex numbers and other math topics. Should you have to have advice on linear inequalities or beginning algebra, zi255.com is certainly the best site to check-out! A good first step in simplifying expressions with exponents such as this, is to look to group like terms together, then proceed. 3 ? 2 ? a2a ? b4b2 = 6 ? a3 ? b6 = 6a3b6 b) Simplify (2a3b2) 2.

Basic Simplifying With Neg. Powers Complex Examples. To simplify with exponents, don't feel like you have to work only with, or straight from, the rules for exponents.

It is often simpler to work directly from the definition and meaning of exponents. For instance:. The rules tell me to add the exponents. But I when I started algebra, I had trouble keeping the rules straight, so I just thought about what exponents mean.

The " a 6 " means "six copies of a multiplied together", and the " a 5 " means "five copies of a multiplied together". So if I multiply those two expressions together, I will get eleven copies of a multiplied together.

That is:. Simplifying Expressions. The exponent rules tell me to subtract the exponents. But let's suppose that I've forgotten the rules again. The " 6 8 " means I have eight copies of 6 on top; the " 6 5 " means I have five copies of 6 underneath.

How many extra 6 's do I have, and where are they? I have three extra 6 's, and they're on top. Unless the instructions also tell you to "evaluate", you're probably expected to leave numerical exponent problems like this in exponent form. How many extra copies of t do I have, and where are they? I have two extra copies, on top:. Once you become comfortable with the "how many extras do I have, and where are they? The answers will start feeling fairly obvious to you.

This question is a bit different, because the larger exponent is on the term in the denominator. But the basic reasoning is the same.

How many extra copies of 5 do I have, and where are they? I have six extra copies, and they're underneath:. Whether or not you've been taught about negative exponents, when they say "simplify", they mean "simplify the expression so it doesn't have any negative or zero powers". Some students will try to get around this minus-sign problem by arbitrarily switching the sign to magically get " 5 6 " on top rather than below a " 1 " , but this is incorrect.

I mustn't forget that the " 5 " and the " 3 " are just numbers. Since 3 doesn't go evenly into 5 , I can't cancel the numbers. For the variables, I have two extra copies of x on top, so the answer is:.

Either of the purple highlighted answers should be acceptable: the only difference is in the formatting; they mean the same thing. This is simple enough: anything to the zero power is just 1. The parenthetical portion still simplifies to 1 , but this time the "minus" is out in front of the parentheses; that is, it's out from under the power, so the exponent doesn't touch it. So the answer in this case is:. I can cancel off the common factor of 5 in the numerical part of the fraction:.

Now I need to look at each of the variables. How many extra of each do I have, and where are they? I have two extra a 's on top. I have one extra b underneath. And I have the same number of c 's top and bottom, so they'll cancel off entirely.

## 4 thoughts on “How to simplify expressions with variables and exponents”

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