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anonymous

  • 5 years ago

how can you write a experession as a single exponent?

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  1. anonymous
    • 5 years ago
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    Depends on the expression

  2. anonymous
    • 5 years ago
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    okay \[3^{2} - 3^{3}\]

  3. anonymous
    • 5 years ago
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    Ok, to do this you will need to factor a bit. Do you know how to factor?

  4. anonymous
    • 5 years ago
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    yes

  5. anonymous
    • 5 years ago
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    Ok, so we can rewrite this expression like this: \[3^2 - 3^3 = 3^2 - (3^2*3)\] Right?

  6. anonymous
    • 5 years ago
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    yes

  7. anonymous
    • 5 years ago
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    Now factor out a \(3^2\) from each term, and what do you get?

  8. anonymous
    • 5 years ago
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    \[3^{5} \right\]

  9. anonymous
    • 5 years ago
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    i mean \[3^{5}\]

  10. anonymous
    • 5 years ago
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    No. \[3^2 - 3^2(3) = 3^2(\frac{3^2}{3^2} -\frac{3^2( 3)}{3^2}) = 3^2(1-3)\]

  11. anonymous
    • 5 years ago
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    Recall how to factor something 5(3) + 5(100) = 5(3+100) = 5(103)

  12. anonymous
    • 5 years ago
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    17-17(23) = 17(1-23) = 17(-22)

  13. anonymous
    • 5 years ago
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    Or if you prefer you can think of it the other way. \[3^2 - 3(2^2) = 1(3^2) - 3(3^2) = -2(3^2)\]

  14. anonymous
    • 5 years ago
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    Ack.. that should be \[3^2 - 3(3^2)\] before the first equals

  15. anonymous
    • 5 years ago
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    Did I lose you?

  16. anonymous
    • 5 years ago
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    yeah alot

  17. anonymous
    • 5 years ago
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    Ok lets try this a different way. Forget what I said before. Ok

  18. anonymous
    • 5 years ago
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    ok

  19. anonymous
    • 5 years ago
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    \[3^2 - 3^3\] \[= 1(3^2) - 3(3^2)\] With me so far?

  20. anonymous
    • 5 years ago
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    Do you see how these two things are equal?

  21. anonymous
    • 5 years ago
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    yes

  22. anonymous
    • 5 years ago
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    Ok, so now I tell you, you have 1x and you subtract 3x, what will you have?

  23. anonymous
    • 5 years ago
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    -3 right?

  24. anonymous
    • 5 years ago
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    -2x

  25. anonymous
    • 5 years ago
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    ok i get it

  26. anonymous
    • 5 years ago
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    So here, you have \(1(3^2)\) and you subtract \(3(3^2)\), what will you have?

  27. anonymous
    • 5 years ago
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    -18

  28. anonymous
    • 5 years ago
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    Well yes, but that's not an expression with 1 exponent.

  29. anonymous
    • 5 years ago
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    Although you could write it as \(-18^1\) if you want to be a smart retrice;p

  30. anonymous
    • 5 years ago
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    I think they want you to write it as \(-2(3^2)\)

  31. anonymous
    • 5 years ago
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    ok

  32. anonymous
    • 5 years ago
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    I could be wrong though.

  33. anonymous
    • 5 years ago
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    how?

  34. anonymous
    • 5 years ago
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    it should be 3^-1

  35. anonymous
    • 5 years ago
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    Wait a minute, that is not correct

  36. anonymous
    • 5 years ago
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    im confused now

  37. anonymous
    • 5 years ago
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    It's -18 or \(-2(3^2)\). It's the same number, it just depends on how your teacher wants to see it.

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