Homework Help: Math: Algebra: Exponents of Variables

The last lesson explained how to simplify exponents of numbers by multiplying as shown below. You know that 3 squared is the same as 1 * 3 * 3.

Exponents of variables work the same way - the exponent indicates how many times 1 is multiplied by the base of the exponent. Take a look at the example below.

The first problem we will work on is below. It doesn't contain a variable, but it will help us to learn how to simplify a similar problem with a varable in place of the first 3.

Normally, you would simplify this problem by simplifying the inside of the parentheses first:

Then, simplify the exponent outside the parentheses.

This method gives a correct answer, but there is an easier way.

We will be solving the same problem again:

This time, instead simplifying inside of the parentheses first, we will "distribute" the exponent of the parentheses to the inside of the parentheses.

Now the only thing left to do is simplify the exponent that is left.

As you can see this method also gives an answer of 729.

The first example with variables is

We will try simplifying it the first way, by simplifying the inside of the parentheses followed by simplifying the exponent on the outside.

Now that the inside is simplified, the exponent on the parentheses indicates that the expression is equivalent to a 1 multiplied by the parentheses, three times. As you can see x is being multiplied 6 times, hence the answer x to the sixth power.

Again, the problem we are working is

As with the second number example earlier in this lesson, simply multiply the two exponents:

Then remove the parentheses, and as you can see the answer is the same.

Homework Help: Math: Algebra

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