raphaelll
  • raphaelll
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
zepdrix
  • zepdrix
So the first one is this, ya? \(\large\rm 5^5\cdot5^5\)
raphaelll
  • raphaelll
Yup thats the first one
zepdrix
  • zepdrix
Here is our rule of exponents that will be very helpful to use: \(\large\rm x^a\cdot x^b=x^{a+b}\)

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zepdrix
  • zepdrix
Notice that when we apply this rule, the `base` stays the same.
zepdrix
  • zepdrix
Any ideas how we can use this? :)
raphaelll
  • raphaelll
umm, i just take 5 and add the two powers together?
zepdrix
  • zepdrix
\[\large\rm 5^\color{orangered}{5}\cdot5^\color{orangered}{5}=5^{\color{orangered}{5+5}}\]Mmm good!
raphaelll
  • raphaelll
thanks! how do i go about doing the second question since there is a negative power?
zepdrix
  • zepdrix
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?
raphaelll
  • raphaelll
oh i see, is it also just addition if division is the middle step?
zepdrix
  • zepdrix
division is a little different: \(\large\rm x^a\div x^b=x^{a-b}\)
zepdrix
  • zepdrix
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.
raphaelll
  • raphaelll
okay thank you! so for multiplication it is just adding the two powers, and for division it is subtracting the two powers
zepdrix
  • zepdrix
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 :)
raphaelll
  • raphaelll
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
zepdrix
  • zepdrix
Can you write out the question? :o That might make it easier for us.
raphaelll
  • raphaelll
26.9 x 463 000 and 55.18 divided by 620
zepdrix
  • zepdrix
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.
zepdrix
  • zepdrix
|dw:1441616656957:dw|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:
zepdrix
  • zepdrix
|dw:1441616745335:dw|
zepdrix
  • zepdrix
I'm going to write a decimal after that number,|dw:1441616795550:dw|
zepdrix
  • zepdrix
The number that goes in the \(\large\rm \triangle\) is the number of places that you moved the decimal.
zepdrix
  • zepdrix
|dw:1441616863094:dw|Decimal always starts here by the way.
zepdrix
  • zepdrix
|dw:1441616886977:dw|Looks like we had to move the decimal 7 places.
zepdrix
  • zepdrix
|dw:1441616919559:dw|Bam ok we got the first one done!
zepdrix
  • zepdrix
Any confusion there? :o
raphaelll
  • raphaelll
no actually you explained that really well!
zepdrix
  • zepdrix
55.18 divided by 620 This one is a little different... doing the division we end up with: \(\large\rm 0.089\)
zepdrix
  • zepdrix
So what number goes in the \(\large\rm \square\), what do you think? :o
raphaelll
  • raphaelll
8 because it is greater than 1 but less than 10
zepdrix
  • zepdrix
Ok good! We want to keep all of the important values that follow the 8 as well.\[\LARGE\rm 8.9\times10^?\]
raphaelll
  • raphaelll
10 to the power of 3?
zepdrix
  • zepdrix
|dw:1441617458964:dw|Hmm, I don't think we moved 3 place values! :)
raphaelll
  • raphaelll
oh yup my bad, i looked at the diagram from before thinking the decimal started from the end
zepdrix
  • zepdrix
So, 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
  • raphaelll
okay 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
raphaelll
  • raphaelll
negative 2*
zepdrix
  • zepdrix
\[\LARGE\rm 8.9\times10^{-2}\]Yay good job team \c:/
raphaelll
  • raphaelll
thank you so much for all your help! will definitely be in touch if i ever need more help :P

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