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Multiplying & Dividing Terms With Exponents

In this video, we are going to look at how to multiply and divide terms with exponents. After you finish this lesson, view all of our Pre-Algebra lessons and practice problems. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.

Example of Multiplying Terms with Exponents

To solve the following:
3^2 \times 3^3
We add the exponents when the bases are the same, to get
3^5
To solve something more complex such as
(3x^3y^2)(4x^4y^5)
we multiply the constants first, then we multiply the terms with the same base to get
12x^7y^7
To solve the following:
3^4 \div 3^2
we subtract the exponents when the bases are the same, to get
3^2

Other examples:

Multiplying Terms that have Exponents and the Same Base
x^a \times x^b = x^{a+b}
3^9 \times 3^4 = 3^{9+4} = 3^{13}

Dividing Terms that have Exponents and the Same Base
x^a \div x^b = x^{a-b}
3^9 \div 3^4 = 3^{9-4} = 3^{5}

Examples of Properties of Exponents

Example 1

(9a^{3}b^{2}c{4})(3a^{4}b^{6}c^{3})

First, we simply multiply the constants

9 \times 3 = 27

Then, we multiply the terms with the same base

a^{3+4}=a^{7}

b^{2+6}=b^{8}

c^{4+3}=c^{7}

Now, we have:

27a^{27}b^{8}c^{7}

Example 2

18x^{8} \div 6x^{2}

First we have to divide the constants

\dfrac{18x^{8}}{ 6x^{2}}= \dfrac{ 6x^{8}}{ x^{2}}

In dividing, we just have to subtract the exponents

6x^{8-2}

Now, we have:

6x^{6}

Video-Lesson Transcript

In this video, we are going to look at how to multiply and divide terms with exponents.

Let’s go to Multiplication first.

We have 3^2 \times 3^3

So we have 3^2 \times 3^3 = 3 \times 3 \times 3 \times 3 \times 3

= 3^5

Another example, x^4 \times x^2

So instead of writing it all out, we just have to add the exponents.

In Multiplying, we just have to add the exponents and will have 4 + 2 = 6

The final answer is x^6

Next, we have x^3 x y^2.

They have different base so the final answer is just x^3 y^2

Let’s move on to a more complicated one.

\big(3 x^3 y^2\big) \big(4 x^4 y^5\big)

You can multiply this simply by multiplying the two coefficients first 3 \times 4 = 12

Then, the two with the similar base x^{3 + 4} = x^7

We will have x^7

Then y^{2 + 5} = y^7

And the answer is y^7

Our final answer is 12 x^7 y^7

Now, let’s move on to Division.

\dfrac{3^4}{3^2}

So = \dfrac{3 \times 3 \times 3 \times 3}{3 \times 3}

We’ll cancel out and will come up with = 3^2

So in Dividing, we just have to subtract the exponents.

Another example is \dfrac{5^6}{5^2}

It should be 5^{6 - 2} = 5^4

And we’ll have 5^4

Learn How To Multiply And Divide Terms With Exponents