# Pre-Algebra : Product Rule of Exponents

## Example Questions

### Example Question #1 : Product Rule Of Exponents

Simplify:

Explanation:

When multiplying variables with exponents, we must remember the Product Rule of Exponents:

Step 1: Reorganize the terms so the terms are together:

Step 2: Multiply  :

Step 3: Use the Product Rule of Exponents to combine  and and then and :

### Example Question #1 : Product Rule Of Exponents

Simplify the following.

Explanation:

The Product of Powers Property states when we multiply two powers with the same base, we add the exponents.

In this case, the exponents are 2 and 5

### Example Question #1 : Product Rule Of Exponents

Simplify the following expression:

Explanation:

The exponent represents how many times the term is being multiplied. So, for example, means and would be

So the first term

And the second term

Since the two terms are only separated by parentheses, they are being all multiplied together.

First multiply the coefficients,

We also have a total of 4 's and 2 's all being multipled together.

### Example Question #2 : Product Rule Of Exponents

Simplify the following expression:

Explanation:

The exponent represents how many times the term is being multiplied. So, for example, means and would be

So the first term  =

And the second term =

Since the two terms are only separated by parentheses, they are being all multiplied together.

First multiply the coefficients,

We also have a total of 8 's and 4 's all being multipled together.

### Example Question #2 : Product Rule Of Exponents

Simplify the following expression:

Explanation:

In the last few problems, we saw one way to multiply terms with exponents.

Another way to explain what we did is to say: "When you MULTIPLY terms together, simplify by ADDING the exponents of each variable."

Here's what that looks like in this case:

First multiply the coefficients:

Then ADD the exponents of the variables to simplify. In the first term, the exponent on the  is 2. In the second term the exponent is 1. So we ADD and have .

Only the second term has the variable and its exponent is 5. There is nothing to add onto that (because there are no 's in the first term), so it stays .

Remember, this is all being multiplied together, so the final answer is

### Example Question #3 : Product Rule Of Exponents

Simplify the following expression:

Explanation:

Remember the rule:

"When you MULTIPLY terms together, simplify by ADDING the exponents of each variable."

Here's what that looks like in this case:

First multiply the coefficients:

Then ADD the exponents of the variables to simplify. In the first term, the exponent on the  is 2. In the second term the exponent is 1. So we ADD  and just have .

In the first term, the exponent on the is 3. In the second term the exponent is 6. So we ADD  and just have .

In the first term, the exponent on the  is 2. In the second term the exponent is 2. So we ADD  and just have .

Remember, all these parts are being multiplied together, so the final answer is

### Example Question #4 : Product Rule Of Exponents

Simplify the following expression:

Explanation:

The exponent represents how many times the term is being multiplied. So, for example, means and would be

So the first term

And the second term

Since the two terms are only separated by parentheses, they are being all multiplied together.

First multiply the coefficients,

We also have a total of 6 's and 1  all being multipled together.

### Example Question #5 : Product Rule Of Exponents

Simplify the following expression:

Explanation:

The exponent represents how many times the term is being multiplied. So, for example, means and would be

So the first term

And the second term

Since the two terms are only separated by parentheses, they are being all multiplied together.

First multiply the coefficients,

We also have a total of  's all being multipled together.

Simplify:

Explanation:

### Example Question #1 : Product Rule Of Exponents

Which of the following is equal to ?