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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.
For example:
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}

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