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When NOT to Add or Subtract Exponents
One of the most common algebraic mistakes that a beginner usually makes is trying to add or subtract exponents from each other by adding or subtracting the powers. For example, if you were given the problem 2^2 + 2^3, you might think that the answer is 2^5. This is incorrect. In order to figure out the correct answer to this problem, you would need to calculate both terms – 2^2 is 4, and 2^3 is 8. Then you would add them together – 4 + 8 = 12. So 2^2 + 2^3 = 12, which is not the same as 2^5.
This mistake is very common when variables enter the picture. For example, you might think that x^2 + x^2 = x^4. As explained above, this is not correct. When you’re adding and subtracting exponents, make sure that you don’t assume that you can always add or subtract as long as the bases are the same!
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Adding and Subtracting Like Terms
So when can you add and subtract exponents? You can only add and subtract exponents when they are made of “like terms.” That means that both the base and the power must be the same.
For example, take the problem 2(x^2) + 3y + x^2 + 4(y^2). Which of these are like terms? You might think that 3y and 4(y^2) are like terms because they both include the variable y. However, remember that like terms need to have the same base and power. Although the base (y) is the same, the power is not. 3y is raised to the power of 1, and 4(y^2) is raised to the power of 2. The two like terms in this problem are 2(x^2) and x^2, because they both have the base of x and are raised to the power of 2.
Therefore, to add the exponents in this problem, you can only combine the two like terms 2(x^2) and x^2, which together equal 3(x^2). So 2(x^2) + 3y + x^2 + 4(y^2) is really the same thing as 3(x^2) + 3y + 4(y^2).
Adding exponents can be tricky, but if you follow the directions in this study guide, you’ll always make sure to only add like terms.