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Exponents of Variables

The problem below has two key differences.

  • First, it has a term with two variables, and as you can see the exponent from outside the parentheses must multiply EACH of them.
  • Second, there is a negative sign inside the parentheses. Since the exponent on the parentheses is 3, the negative sign is written in front of the term three times. Then the multiple signs are simplified.

Both the problem above and below this have a negative sign inside a set of parentheses which is raised to some power. If you did a lot of these you'd notice that when the parentheses are raised to an odd power such as 3, the answer will be negative. If the parentheses are raised to an even power like the one below, the answer will be positive.

The last problem, shown below has a negative sign outisde the parentheses. Again, because of the Order of Operations which is presented in a later lesson, the exponent must be simplified before you do anything with the negative sign. Look at the work below:

Note that even though the exponent on the parentheses was a 4 which is an even number, the final answer is negative. This is because the negative sign was outside of the parentheses, not inside as in the previous example.

The next page has resources and worksheets for this lesson.


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