Exponent Laws Examples
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.
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:
a2 x (ab)3 = a2 x a3b3
= a2 + 3 b3
As for the next law, here are some examples:
20 ÷ e0 = 1 ÷ 1
(a10 qr+s z-10 + 5b)0 = (whatever)0
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.
Click play to watch
Math Video Transcript
This lesson shows you some example questions on the exponent laws. Now, let's simplify the following.
Let's consider this example, 4 to the power of 3 multiply by 2 to the power of 4.
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.
Therefore, we need to find a way to make these bases to be the same.
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.
Therefore, we can replace 4 with 2 to the power of 2.
Alright, notice that to proceed, we need to simplify this term.
To do so, we can use this law.
Before we use it, let's match the colors first.
Now, 2 to the power of 2, to the power 3 is equals to, 2 to the power of 2 multiply by 3.
2 multiply by 3 gives 6.
Now, we can use this exponent law to further simplify these terms. Let's match the colors first.
2 to the power of 6 multiply 2 to the power of 4, gives 2 to the power 6 plus 4.
Now, 6 plus 4 gives 10. This is the simplest term. So, the answer is 2 to the power of 10.
Next example, let's simplify this.
To do so, we can use this exponent law.
Now, 3 to the power of 2 to the power of 3 is equals to, 3 to the power of 2 multiply by 3.
2 multiply by 3 gives 6.
Next, let's simplify this term.
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.
Now, negative 3 multiply by 4 gives negative 12.
To simplify further, we can use this exponent law.
Let's match the colors first.
Now, by using the exponent law to simplify these terms, we get 3 to the power of 6 plus negative 12.
Notice that, positive multiply by negative gives negative.
With this, when we multiply these terms, we get 3 to the power of 6 minus 12.
6 minus 12 gives negative 6. Now we have 3 to the power of negative 6.
It is better not to leave the answer in the form of negative exponent. So let’s change this to a positive exponent term.
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.
Alright, next example.
Let's simplify this term.
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.
Similarly, q to the power of 8 divides by q to the power of 7 gives q to the power of 8 minus 7.
Let's put this term back.
Now, 5 minus 2 gives 3.
Similarly, 8 minus 7 gives 1.
It is a good practice to write, q to the power of 1 as "q". So, we can remove the number 1 here.
We can no longer simplify this term. So, the answer is 2 p to the power of 3 q.
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.
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