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gabbyalicorn

  • one year ago

Which value of b solves the equation?

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  1. gabbyalicorn
    • one year ago
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  2. gabbyalicorn
    • one year ago
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    I'm sorry! I don't want to be a burden on you but, @Luigi0210 could you help me with some more problems, please? :3

  3. Luigi0210
    • one year ago
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    Oh, that should be simple. Do you know what to do when you encounter a negative exponent?

  4. gabbyalicorn
    • one year ago
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    Kind of....

  5. Luigi0210
    • one year ago
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    The rule says, when you have a negative exponent you are allowed to flip it to make it positive. Sound familiar?

  6. gabbyalicorn
    • one year ago
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    I thought thats only with -5-(-5) ? They cancel out.

  7. Luigi0210
    • one year ago
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    That's a different rule (: But what I mean, is, let's say you have something like \(\Large 5^{-2} \), you are allowed to flip it so that negative 2 is positive again, like so: \(\huge \frac{1}{5^2} \) And the opposite can be done as well

  8. gabbyalicorn
    • one year ago
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    Oh, that...I've seen that before...

  9. gabbyalicorn
    • one year ago
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    But I don't get the B part, tho.

  10. Luigi0210
    • one year ago
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    B is just a variable, like x, that you have to solve, so let's solve it: So let's flip everything to make that exponent positive \(\Large \frac{1}{b^3} = 216 \) Now, let's get rid of that cube: \(\Large (\frac{1}{b^3})^{1/3}=(216)^{1/3}\) Which leaves us with \(\Large \frac{1}{b} = 6\) make sense so far?

  11. gabbyalicorn
    • one year ago
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    Somewhat.

  12. Luigi0210
    • one year ago
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    What are you confused on?

  13. gabbyalicorn
    • one year ago
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    What's the 1/3 suppose to represent? The exponent. If it is. did u do anything to the 216? (like subtract or divide)

  14. Luigi0210
    • one year ago
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    Wait, I think I made an error, I wasn't suppose to flip that 1/216. Sorry, it'll just be \(\Large \frac{1}{b}=\frac{1}{216} \) And yes, that 1/3 is considered an exponent in this certain problem. The 216, I took the cubic root of it along with the 1/b^3

  15. gabbyalicorn
    • one year ago
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    Okay.

  16. Luigi0210
    • one year ago
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    \(\Large \frac{1}{b^3} =\frac{1}{216} \) \(\Large (\frac{1}{b^3} )^{1/3} = (\frac{1}{216})^{1/3}\) \(\Large \frac{1}{b} =\frac{1}{6} \) Now flip them: \(\Large b=6 \) Which, if you plug it in, would make the statement true

  17. Luigi0210
    • one year ago
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    Sorry if I went a bit quick >><

  18. gabbyalicorn
    • one year ago
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    No worries! :) Is the problem asking what number (b) equals to 216

  19. Luigi0210
    • one year ago
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    Yes, which is the same as 1/216, which would be 6 with that negative exponent.

  20. gabbyalicorn
    • one year ago
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    but couldn't we just do 216 ÷ 2 and then we will find out what b equals

  21. Luigi0210
    • one year ago
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    216/2? That's 108?

  22. gabbyalicorn
    • one year ago
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    yes, it is.

  23. Luigi0210
    • one year ago
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    How is that 6? o.O

  24. gabbyalicorn
    • one year ago
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    oh, b is suppose to equal to 6?

  25. Luigi0210
    • one year ago
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    Yea, 6^3=216, and 6^{-3} = 1/216

  26. gabbyalicorn
    • one year ago
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    oooooooooooh! The answer is 6!

  27. Luigi0210
    • one year ago
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    Yea, I even showed you how to solve it <,<

  28. gabbyalicorn
    • one year ago
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    :o ^///^ sorry! I just started to get it cX

  29. gabbyalicorn
    • one year ago
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    Thank you.

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