Multiplication and Division of Exponents
By John Brooks, M.A.
You can find John on Veditz at https://veditz.org/john-brooks
You can find John’s ASL Video lesson on Multiplication and Division of
Exponents at:
https://support.veditz.org/hc/en-us/articles/222888667
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Hello! Welcome to this video! In this video we will work on
multiplication and division of Exponents.
We have here two examples.
33 x 32
How do we break down 3 to the third power? 3 x 3 x 3. This is
because we have 3 powers. If we have 32, that means we have
two 3’s. We can now use this information to solve.
Here we have 3 products to multiply. Then, we have 2 more to
multiply. So we take these together and now we have 5
products.
We can use a calculator or figure it out by hand. The answer is
243. But there is a better way to work with multiplication of
exponents.
© 2016 Veditz.org and John Brooks
If you paid close attention earlier, you may have caught a hint.
We can add the exponents.
3 to the 3rd power plus 2nd power. This is because we have 5 3’s
here. It is a nice shortcut. This equates to 3 to the 5th power.
If you’re curious about the calculation… 3 to the 5th power will
give the same answer, 243. The number with exponent is more
widely accepted when multiplying exponents.This is because
when you multiply exponents, the numbers can become large.
It can become very time consuming to calculate the actual
number. So this is a better method as it saves time and is more
accurate. So now we’ve covered the multiplication of
exponents example.
Let’s move forward to division. We have here the same
numbers. 3 to the 3rd power over 3 squared.
We will again break it down. We get the same result for each
coefficient and exponent. 3 cubed is equal to 3 times 3 times 3.
3 squared is equal to 3 times 3. We can now take that and use
for the next step.
This time we are dividing so let’s put the numbers in fraction
form. This is because we are following the exponent numbers.
© 2016 Veditz.org and John Brooks
Then we can multiply across. 3 times 3 times 3. This equals 27.
3 times 3. This equals 9. This equals 3.
Or, we have another better way to divide exponents. Here is a
hint. In the multiplication example, we added the exponent
values. So think about the relationship between multiplication
and division.
They are opposite. So what is the opposite of addition?
Subtraction! Here we have a coefficient of 3, with exponents of
3 minus 2. We have one left. 3 to the first power is equal to 3.
This is the same answer.
So now you have an idea of how to multiply and divide
exponents.
Thank you for watching!
© 2016 Veditz.org and John Brooks