Product Rule of Exponents - Pre-Algebra

Use the product rule of exponents, which states that when multiplying expression(s) with the same base, you add the exponents together:

Therefore the correct answer is .

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

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.

The final answer is

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.

The final answer is

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.

The final answer is

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.

The final answer is

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

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

Distribute the to each of the terms and add them.

Remember that when multiplying variables with exponents, the following property holds true:

With this knowledge, we can solve the problem:

The answer is .

The general rule for multiplying terms with exponents is that we add the exponents together. In this case the exponents are and , and . is just : anything to the first power is itself.

The product rule tells us that if we're multiplying 2 terms with exponents, we add the exponents. However, that is only applicable for 2 terms with the same base. In this case, our bases are different variables, so we can't use the product rule. This expression is as simplified as possible.

To simplify it helps to understand what it means. just means x times itself 3 times, . means multiply times itself, or . We can simplify that by multiplying and . Multiplying both terms together gives us . This is a 9 and 5 x's being multiplied together, or .

The product rule states that when two like bases with the same power are being multiplied, we add the powers together and preserve the base. In mathematical language, . If constants are present in front of either base we multiply them as usual.

Combine using the power rule:

Combine the parenthesis:

Factor fully:

The product rule of exponents states that we can multiply two exponents with the same base by adding the exponents. The exponents of different bases cannot be summed, therefore our term will not change.

Therefore, the simplest form of the expression is

which can be written as

When you multiply exponents with the same base, you add the exponents:

When you multiply exponents with the same base, you add the exponents:

When you multiply exponents with the same base, you add the exponents: