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Spring98

  • one year ago

Which expression is equivalent to 3^2 • 3^–5? A. 1/3^3 B. 1/3^7 C. 1/3^-3 D. 1/3^-7

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  1. jim_thompson5910
    • one year ago
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    Use the rule \[\LARGE x^{\color{red}{a}}*x^{\color{blue}{b}} = x^{\color{red}{a}+\color{blue}{b}}\]

  2. jim_thompson5910
    • one year ago
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    For example \[\LARGE x^{\color{red}{2}}*x^{\color{blue}{3}} = x^{\color{red}{2}+\color{blue}{3}}=x^{5}\]

  3. Spring98
    • one year ago
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    so is it C?

  4. jim_thompson5910
    • one year ago
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    what do you get when you use that rule (ignore the answer choices right now)

  5. Spring98
    • one year ago
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    -3

  6. jim_thompson5910
    • one year ago
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    write out the whole thing, not just the exponent

  7. Spring98
    • one year ago
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    |dw:1442278377207:dw|

  8. jim_thompson5910
    • one year ago
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    I meant to include the base

  9. Spring98
    • one year ago
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    why?

  10. jim_thompson5910
    • one year ago
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    look back at the rule I posted

  11. Spring98
    • one year ago
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    yes it's addition

  12. Spring98
    • one year ago
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    i know

  13. jim_thompson5910
    • one year ago
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    so what does \(\LARGE 3^2*3^{-5}\) turn into when you use that rule?

  14. Spring98
    • one year ago
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    3^-3

  15. jim_thompson5910
    • one year ago
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    good

  16. jim_thompson5910
    • one year ago
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    next comes the rule \[\LARGE x^{-a} = \frac{1}{x^a}\]

  17. Spring98
    • one year ago
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    ohh so it's 1/3^-3

  18. Spring98
    • one year ago
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    @jim_thompson5910

  19. jim_thompson5910
    • one year ago
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    close

  20. jim_thompson5910
    • one year ago
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    do you see in the last rule how the `-a` exponent turned into `a` (without the negative) ?

  21. Spring98
    • one year ago
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    yes

  22. jim_thompson5910
    • one year ago
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    so basically that rule is saying "if the exponent is negative, you take the reciprocal of the base to make the exponent positive"

  23. jim_thompson5910
    • one year ago
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    example \[\LARGE 2^{-7} = \frac{1}{2^7}\]

  24. Spring98
    • one year ago
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    ok so that means it is not negative anymore so that the answer will be 1/3^3 right?

  25. jim_thompson5910
    • one year ago
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    yes, \[\LARGE 3^{-3} = \frac{1}{3^3}\]

  26. Spring98
    • one year ago
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    thank you very much!!!

  27. jim_thompson5910
    • one year ago
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    no problem

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