An exponent indicates the amount of times a number (or variable) should be multiplied by itself. For example, .

In this instance, .

Simplify the following expression:

To combine these, we need to multiply the coefficients and add our exponents.

For any nonzero and for any , .

Also, any negative number raised to the power of an odd number is equal to the opposite of the same power of its absolute value.

Combine these concepts:

Since ,

the reciprocals are in reverse order of this:

Their opposites reverse again:

Or, equivalently,

.

To multiply variables with exponents, we will use the following formula:

Now, let’s combine the following:

Start by distributing the exponents into their respective terms. Recall that when an exponent is raised to an exponent, you will need to multiply the exponents together.

Next, multiply like terms together. Recall that when you multiply numbers that have the same base, you will need to add the exponents together.

To divide variables with exponents, we will use the following formula:

Now, let’s divide. We get

has 6, an even number, as an exponent, so is a positive number, and it can be calculated by taking sixth power of 3.

is the (negative) opposite of the sixth power of 3.

Therefore,

and

.

Remember that for negative exponent values, you "flip" the number over the bar of the fraction of which it is a part. When you do this, you then make its power positive. You should always start by doing this. It makes it easier for most students to understand the reductions that follow upon that.

Thus, for your value, you know:

Combine your like variables first. You do this by adding their exponents:

Luckily, there is no canceling for you to do!

For any nonzero and for any , .

Since ,

we can reverse the order when taking their reciprocals:

That is, .