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raphaelll
 one year ago
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
raphaelll
 one year ago
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

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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0So the first one is this, ya? \(\large\rm 5^5\cdot5^5\)

raphaelll
 one year ago
Best ResponseYou've already chosen the best response.0Yup thats the first one

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0Here is our rule of exponents that will be very helpful to use: \(\large\rm x^a\cdot x^b=x^{a+b}\)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0Notice that when we apply this rule, the `base` stays the same.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0Any ideas how we can use this? :)

raphaelll
 one year ago
Best ResponseYou've already chosen the best response.0umm, i just take 5 and add the two powers together?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0\[\large\rm 5^\color{orangered}{5}\cdot5^\color{orangered}{5}=5^{\color{orangered}{5+5}}\]Mmm good!

raphaelll
 one year ago
Best ResponseYou've already chosen the best response.0thanks! how do i go about doing the second question since there is a negative power?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.08 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?

raphaelll
 one year ago
Best ResponseYou've already chosen the best response.0oh i see, is it also just addition if division is the middle step?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0division is a little different: \(\large\rm x^a\div x^b=x^{ab}\)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.06 to the power of 7 divided by 6 to the power of 12 \[\large\rm 6^7\div6^{12}=6^{712}\] 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.

raphaelll
 one year ago
Best ResponseYou've already chosen the best response.0okay thank you! so for multiplication it is just adding the two powers, and for division it is subtracting the two powers

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0Yes! You might be able to see a connection between the multiplication and division... if you really think about it. Not a big deal though :)

raphaelll
 one year ago
Best ResponseYou've already chosen the best response.0you 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

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0Can you write out the question? :o That might make it easier for us.

raphaelll
 one year ago
Best ResponseYou've already chosen the best response.026.9 x 463 000 and 55.18 divided by 620

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0For 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.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441616656957:dwSo 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:

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0I'm going to write a decimal after that number,dw:1441616795550:dw

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0The number that goes in the \(\large\rm \triangle\) is the number of places that you moved the decimal.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441616863094:dwDecimal always starts here by the way.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441616886977:dwLooks like we had to move the decimal 7 places.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441616919559:dwBam ok we got the first one done!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0Any confusion there? :o

raphaelll
 one year ago
Best ResponseYou've already chosen the best response.0no actually you explained that really well!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.055.18 divided by 620 This one is a little different... doing the division we end up with: \(\large\rm 0.089\)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0So what number goes in the \(\large\rm \square\), what do you think? :o

raphaelll
 one year ago
Best ResponseYou've already chosen the best response.08 because it is greater than 1 but less than 10

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0Ok good! We want to keep all of the important values that follow the 8 as well.\[\LARGE\rm 8.9\times10^?\]

raphaelll
 one year ago
Best ResponseYou've already chosen the best response.010 to the power of 3?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441617458964:dwHmm, I don't think we moved 3 place values! :)

raphaelll
 one year ago
Best ResponseYou've already chosen the best response.0oh yup my bad, i looked at the diagram from before thinking the decimal started from the end

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0So, what's different about this problem is that ... since we're moving the decimal to the `right`, the exponent on the 10 will be `negative`.

raphaelll
 one year ago
Best ResponseYou've already chosen the best response.0okay so if the decimal is moved to the right it is negative whereas to the left is positive, so the answer is 10 to the power of 2

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0\[\LARGE\rm 8.9\times10^{2}\]Yay good job team \c:/

raphaelll
 one year ago
Best ResponseYou've already chosen the best response.0thank you so much for all your help! will definitely be in touch if i ever need more help :P
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