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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

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  1. zepdrix
    • one year ago
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    So the first one is this, ya? \(\large\rm 5^5\cdot5^5\)

  2. raphaelll
    • one year ago
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    Yup thats the first one

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

  4. zepdrix
    • one year ago
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    Notice that when we apply this rule, the `base` stays the same.

  5. zepdrix
    • one year ago
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    Any ideas how we can use this? :)

  6. raphaelll
    • one year ago
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    umm, i just take 5 and add the two powers together?

  7. zepdrix
    • one year ago
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    \[\large\rm 5^\color{orangered}{5}\cdot5^\color{orangered}{5}=5^{\color{orangered}{5+5}}\]Mmm good!

  8. raphaelll
    • one year ago
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    thanks! how do i go about doing the second question since there is a negative power?

  9. zepdrix
    • one year ago
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    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?

  10. raphaelll
    • one year ago
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    oh i see, is it also just addition if division is the middle step?

  11. zepdrix
    • one year ago
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    division is a little different: \(\large\rm x^a\div x^b=x^{a-b}\)

  12. zepdrix
    • one year ago
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    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.

  13. raphaelll
    • one year ago
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    okay thank you! so for multiplication it is just adding the two powers, and for division it is subtracting the two powers

  14. zepdrix
    • one year ago
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    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 :)

  15. raphaelll
    • one year ago
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    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

  16. zepdrix
    • one year ago
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    Can you write out the question? :o That might make it easier for us.

  17. raphaelll
    • one year ago
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    26.9 x 463 000 and 55.18 divided by 620

  18. zepdrix
    • one year ago
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    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.

  19. zepdrix
    • one year ago
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    |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:

  20. zepdrix
    • one year ago
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    |dw:1441616745335:dw|

  21. zepdrix
    • one year ago
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    I'm going to write a decimal after that number,|dw:1441616795550:dw|

  22. zepdrix
    • one year ago
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    The number that goes in the \(\large\rm \triangle\) is the number of places that you moved the decimal.

  23. zepdrix
    • one year ago
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    |dw:1441616863094:dw|Decimal always starts here by the way.

  24. zepdrix
    • one year ago
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    |dw:1441616886977:dw|Looks like we had to move the decimal 7 places.

  25. zepdrix
    • one year ago
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    |dw:1441616919559:dw|Bam ok we got the first one done!

  26. zepdrix
    • one year ago
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    Any confusion there? :o

  27. raphaelll
    • one year ago
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    no actually you explained that really well!

  28. zepdrix
    • one year ago
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    55.18 divided by 620 This one is a little different... doing the division we end up with: \(\large\rm 0.089\)

  29. zepdrix
    • one year ago
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    So what number goes in the \(\large\rm \square\), what do you think? :o

  30. raphaelll
    • one year ago
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    8 because it is greater than 1 but less than 10

  31. zepdrix
    • one year ago
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    Ok good! We want to keep all of the important values that follow the 8 as well.\[\LARGE\rm 8.9\times10^?\]

  32. raphaelll
    • one year ago
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    10 to the power of 3?

  33. zepdrix
    • one year ago
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    |dw:1441617458964:dw|Hmm, I don't think we moved 3 place values! :)

  34. raphaelll
    • one year ago
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    oh yup my bad, i looked at the diagram from before thinking the decimal started from the end

  35. zepdrix
    • one year ago
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    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`.

  36. raphaelll
    • one year ago
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    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

  37. raphaelll
    • one year ago
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    negative 2*

  38. zepdrix
    • one year ago
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    \[\LARGE\rm 8.9\times10^{-2}\]Yay good job team \c:/

  39. raphaelll
    • one year ago
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    thank you so much for all your help! will definitely be in touch if i ever need more help :P

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