### Exponent Laws Examples

#### Lesson Objective

This lesson shows you some examples on using the exponent laws that you have learned in the previous lessons.

#### About This Lesson

After learning the exponent laws in the previous two lessons, it's time to learn on how you can apply them.

This lesson shows you some examples on using these laws.

### Study Tips

#### Tip #1

In the last lesson, we have learned three more laws. Let's recall them here. The picture shows one of the law. Here is an example on how to use it:

a^{2} x (ab)^{3} = a^{2} x a^{3}b^{3}

= a^{2 + 3} b^{3}

= a^{5}b^{3}

#### Tip #2

As for the next law, here are some examples:

2^{0} ÷ e^{0} = 1 ÷ 1

= 1

(a^{10} q^{r+s} z^{-10} + 5b)^{0} = (whatever)^{0}

= 1

#### Tip #3

Finally, the picture below shows the last law. Here is an example on how to use it:

Now, watch the following math video to see more examples.

### Math Video

#### Click play to watch

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#### Math Video Transcript

00:00:01.090

This lesson shows you some example questions on the exponent laws. Now, let's simplify the following.

00:00:09.200

Let's consider this example, 4 to the power of 3 multiply by 2 to the power of 4.

00:00:16.190

Now, if we consider this law, we’ll realize that we can not use it because the base for these terms are not the same.

00:00:24.190

Therefore, we need to find a way to make these bases to be the same.

00:00:29.170

To do so, notice that 4 here is equals to, 2 multiply by 2, which is also equals to, 2 to the power of 2.

00:00:39.130

Therefore, we can replace 4 with 2 to the power of 2.

00:00:44.130

Alright, notice that to proceed, we need to simplify this term.

00:00:49.150

To do so, we can use this law.

00:00:53.180

Before we use it, let's match the colors first.

00:00:58.060

Now, 2 to the power of 2, to the power 3 is equals to, 2 to the power of 2 multiply by 3.

00:01:06.150

2 multiply by 3 gives 6.

00:01:12.040

Now, we can use this exponent law to further simplify these terms. Let's match the colors first.

00:01:20.110

2 to the power of 6 multiply 2 to the power of 4, gives 2 to the power 6 plus 4.

00:01:27.050

Now, 6 plus 4 gives 10. This is the simplest term. So, the answer is 2 to the power of 10.

00:01:38.200

Next example, let's simplify this.

00:01:42.140

To do so, we can use this exponent law.

00:01:46:040

Now, 3 to the power of 2 to the power of 3 is equals to, 3 to the power of 2 multiply by 3.

00:01:53.240

2 multiply by 3 gives 6.

00:01:58.240

Next, let's simplify this term.

00:02:02.080

3 to the power of negative 3, to the power of 4 is equals to, 3 to the power of negative 3 multiply by 4.

00:02:10.150

Now, negative 3 multiply by 4 gives negative 12.

00:02:17.000

To simplify further, we can use this exponent law.

00:02:21:110

Let's match the colors first.

00:02:25.010

Now, by using the exponent law to simplify these terms, we get 3 to the power of 6 plus negative 12.

00:02:33.070

Notice that, positive multiply by negative gives negative.

00:02:39.130

With this, when we multiply these terms, we get 3 to the power of 6 minus 12.

00:02:46.060

6 minus 12 gives negative 6. Now we have 3 to the power of negative 6.

00:02:52.220

It is better not to leave the answer in the form of negative exponent. So let’s change this to a positive exponent term.

00:03:00.160

Now, referring to this exponent law. We can see that, 3 to the power of negative 6 is equals to, 1 divides by 3 to the power of 6.

00:03:13.240

Alright, next example.

00:03:16.100

Let's simplify this term.

00:03:19.200

8 divides by 4 gives 2. Now, referring to this exponent law, we can see that, p to the power of 5 divides by p to the power of 2 gives p to the power of 5 minus 2.

00:03:32.200

Similarly, q to the power of 8 divides by q to the power of 7 gives q to the power of 8 minus 7.

00:03:40.010

Let's put this term back.

00:03:42.210

Now, 5 minus 2 gives 3.

00:03:48.210

Similarly, 8 minus 7 gives 1.

00:03:52.230

It is a good practice to write, q to the power of 1 as "q". So, we can remove the number 1 here.

00:04:00.050

We can no longer simplify this term. So, the answer is 2 p to the power of 3 q.

00:04:07.020

That’s all for this lesson. Try out the practice questions for reinforce your understanding.

### Practice Questions & More

#### Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on exponent laws examples or pick your choice of question below.

- Question 1 on the basics on exponent laws
- Question 2 on the basics on exponent laws

#### Site-Search and Q&A Library

Please feel free to visit the Q&A Library. You can read the Q&As listed in any of the available categories such as Algebra, Graphs, Exponents and more. Also, you can submit math question, share or give comments there.