When do you add exponents together

To do the simplification, I can start by thinking in terms of what the exponents mean. The "to the fourth" on the outside means that I'm multiplying four copies of whatever base is inside the parentheses. In this case, the base of the fourth power is x 2. Multiplying four copies of this base gives me:.

Each factor in the above expansion is "multiplying two copies" of the variable. This expands as:. This is a string of eight copies of the variable. This demonstrates the second exponent rule:. Whenever you have an exponent expression that is raised to a power, you can simplify by multiplying the outer power on the inner power:. If you have a product inside parentheses, and a power on the parentheses, then the power goes on each element inside.

For instance:. Warning: This rule does NOT work if you have a sum or difference within the parentheses. Exponents, unlike mulitiplication, do NOT " distribute " over addition. When in doubt, write out the expression according to the definition of the power. For instance, given x — 2 2 , don't try to do this in your head. Instead, write it out; "squared" means "multiplying two copies of", so:. The mistake of erroneously trying to "distribute" the exponent is most often made when the student is trying to do everything in his head, instead of showing his work.

Do things neatly, and you won't be as likely to make this mistake. Now that I know the rule about powers on powers, I can take the 4 through onto each of the factors inside.

I'll need to remember that, with the c , inside the parentheses it's "to the power 1 ". Anything to the power zero is just " 1 " as long as the "anything" it not itself zero. This rule is explained on the next page. In practice, though, this rule means that some exercises may be a lot easier than they may at first appear:.

The x is called the base. The 2 is called the exponent. The first term has a 2 and the second term has a 3. As a result, we cannot simplify this expression any more. The first term has an x and the second term has a y. Therefore, we cannot combine them. But how? To add terms with the same base and exponent, just add the coefficients. This is not to be confused with the product rule. That rule also involves manipulating exponents. However, it is for multiplying exponents together.

Right now we are adding them instead. Sometimes, you'll have lots of terms. To simplify, you combine as many groupings of terms as you can. Sometimes we'll want to rearrange the terms to make this easier. We can do this because of the commutative property of addition. Every student loves a classic game of Jeopardy. Using a customizable template , replace the trivia with questions that give students a chance to practice multiplying exponents, and divide the class into two teams.

Worksheets are a tried-and-true method for developing math fluency in a particular set of skills. They can also be an indicator of student understanding when used as part of a formative assessment strategy. Here are some of our favorites:. For something more unique, try this multiplying polynomials activity.

Cut out the accompanying strips and mix them up. Have students match answers to the correct section on their worksheet after solving the equation and showing their work. As always, take it slow and make sure students understand the basics before things get more complicated. Contents A quick review of exponent rules 4 steps for teaching your students how to multiply exponents Fun multiplying exponents activities for students.

What do earthquakes, the stock market, computer science and nuclear physics all have in common? They all involve multiplying exponents.

There are seven exponent rules: Product of powers rule : Add powers together when multiplying like bases Quotient of powers rule : Subtract powers when dividing like bases Power of powers rule : Multiply powers together when raising a power by another exponent Power of a product rul e: Distribute power to each base when raising several variables by a power Power of a quotient rule : Distribute power to all values in a quotient Zero power rule : Any base raised to the power of zero becomes one Negative exponent rule : To change a negative exponent to a positive one, flip it into a reciprocal Got it?

The bases of the equation stay the same, and the values of the exponents get added together. Then, add the exponents together. Multiplying exponents with different bases and exponents What happens when you want to multiply different exponents with different bases? Multiplying negative exponents It might seem complicated, but multiplying exponents with negative numbers is exactly the same as multiplying exponents with non-negative numbers.

Remember — add exponents with like bases. Just like above, multiply the bases and leave the exponents the same. Prodigy Building math fluency is an important part of making sure students feel confident in high school- and college-level math courses. Exponent War. The classic card game — but with an exponentially fun twist! Exponent Scavenger Hunt.