Question

Simplify the following expressions. Give your answers in power notation where the powers are positive.



8 to the power of -6 x 8 to the power of 2

6 to the power of 7 divided by 6 to the power of 12

Answer 1

So the first one is this, ya? \(\large\rm 5^5\cdot5^5\)

Answer 2

Yup thats the first one

Answer 3

Here is our rule of exponents that will be very helpful to use:
\(\large\rm x^a\cdot x^b=x^{a+b}\)

Answer 4

Notice that when we apply this rule, the `base` stays the same.

Answer 5

Any ideas how we can use this? :)

Answer 6

umm, i just take 5 and add the two powers together?

Answer 7

\[\large\rm 5^\color{orangered}{5}\cdot5^\color{orangered}{5}=5^{\color{orangered}{5+5}}\]Mmm good!

Answer 8

thanks!
how do i go about doing the second question since there is a negative power?

Answer 9

8 to the power of -6 x 8 to the power of 2
\[\large\rm 8^{-6}\cdot8^{2}=8^{-6+2}\]Same thing, addition :)
Remember how to add a negative and positive together?

Answer 10

oh i see, is it also just addition if division is the middle step?

Answer 11

division is a little different: \(\large\rm x^a\div x^b=x^{a-b}\)

Answer 12

6 to the power of 7 divided by 6 to the power of 12
\[\large\rm 6^7\div6^{12}=6^{7-12}\]
Make sure you write the 7 and 12 in the correct locations.
I was forced to write the 7 first because that shows up on the left of the division.
The 7 is smaller, so yes, you should end up with a negative power after you complete the subtraction.

Answer 13

okay thank you! so for multiplication it is just adding the two powers, and for division it is subtracting the two powers

Answer 14

Yes!
You might be able to see a connection between the multiplication and division... if you really think about it. Not a big deal though :)

Answer 15

you wouldn't happen to know anything about scientific notation would you? it's the last two questions on my assignment that i don't understand

Answer 16

Can you write out the question? :o
That might make it easier for us.

Answer 17

26.9 x 463 000

and

55.18 divided by 620

Answer 18

For the first one, when you do the multiplication you get: \(\large\rm 12,454,700\)
This is not scientific notation.
For scientific notation, we want to write this as a number... times some power of 10.

Answer 19

So we want to write the number like this.
The number that goes here \(\large\rm \square\) should be a single digit. something larger than 1, and less than 10.

So when we look at our number, we can see that THIS is the number that goes in the square: