Algebra, with its introduction of letters into math and abstract thinking, causes frustrations for many math students. One if its most daunting concepts is that of exponents, or powers. If you are having trouble remembering what the exponent rules for addition and subtraction are, and how to use them, check out these tips.
Check for Same Variables
When dealing with operations and exponents, the first thing to look for is whether or not the variables involved are the same letter. These are called the "bases," and if they are not the same letter, you cannot do anything to them. For instance, you cannot combine Y^4 (Y to the fourth power) in any way with X^6 (X to the sixth power). The same is also usually true for bases that are numbers. For example, 3^3 cannot be combined with 4^8 without calculating each of them first.
Once you have figured out that the bases are the same letter, look at the operation sign. If it is addition, you then need to look at the exponents/powers. If they are the same for both bases, such as X^2 + 3X^2, then you can add them together by combining like terms. Do this by adding the coefficients, the numbers in front of each base. For example, in this case 1 + 3 would give you 4, and you would end up with 4X^2. When adding like terms with exponents, the powers just describe the terms and do not change. It is like saying 1 apple + 3 apples makes 4 apples. This is different from the multiplication and division rules where the exponents DO change.
If, on the other hand, the powers are different, you cannot do anything. For example, you could not do 6X^3 + 2X^8 because 3 and 8 are not the same. It would be like trying to total apples and oranges together as apples.
The same idea applies to the subtraction exponent rule. If the powers of the bases are not the same, you cannot perform the subtraction. For instance, you would not be able to do 2X^5 - 3X^2 because 5 and 2 are not the same. If the powers are the same, however, you subtract the coefficients of the like terms just as you would add them. So, 4X^5 - 2X^5 would be 2X^5 because 4 minus 2 = 2.
If there are more than two terms, rewrite subtractions as adding negatives. For instance, you would rewrite 3X^4 - 6X^4 + 2X^4 - 8X^4 as 3x^4 + - 6X^4 + 2X^4 + - 8X^4. You can then do all of the math at once: 3 +-6 +2 +-8 = -9, and the answer would be -9X^4.
If you have several terms where some of which have the same base and exponent and some of which do not, regroup them and place like terms and like powers next to each other. Remember, however, that the sign in front of a term must travel with it so that positives and negatives stay the way that they are. For example, 3X^3 + 2X^5 - 4 X^3 would be regrouped as 3X^3 - 4X^3 + 2X^5 so that you can combine the Xs to the third power. In the end, the expression would be simplified as 2X^5 - X^3. The 2X^5 is placed in the front because an expression must always start with a positive term if possible.
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