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xKingx

  • 2 years ago

How do you write this in simplest form?

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  1. xKingx
    • 2 years ago
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  2. geoffb
    • 2 years ago
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    \[\LARGE (b^{x})^{y} = b^{x \times y}\]

  3. geoffb
    • 2 years ago
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    Remember the outside exponent also applies to the 8.

  4. mathgirl73
    • 2 years ago
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    everything must be raised to -2/3 power . when raise a product by a power you multiply the exponents

  5. xKingx
    • 2 years ago
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    @geoffb Can you explain how I'd use that formula with this problem?

  6. mathgirl73
    • 2 years ago
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    |dw:1354925885023:dw|

  7. mathgirl73
    • 2 years ago
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    |dw:1354925885023:dw|

  8. xKingx
    • 2 years ago
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    Can you explain what you did in each step so I can make sure I understand it?

  9. mathgirl73
    • 2 years ago
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    from the image the exponents looks negative.

  10. xKingx
    • 2 years ago
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    They are

  11. mathgirl73
    • 2 years ago
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    everything has to be raised by the power that is outside the parentheses. so -2/3

  12. mathgirl73
    • 2 years ago
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    everything has to be raised by the power that is outside the parentheses. so -2/3

  13. mathgirl73
    • 2 years ago
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    8 raised to the -2/3 and a^-3 raised to the -2/3

  14. mathgirl73
    • 2 years ago
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    so you have 8^-2/3

  15. mathgirl73
    • 2 years ago
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    you have to multiply a^-3 by -2/3

  16. mathgirl73
    • 2 years ago
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    so you get in the numerator -3 times -2 = 6 and the denominator 3 times 1=3

  17. mathgirl73
    • 2 years ago
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    so you get in the numerator -3 times -2 = 6 and the denominator 3 times 1=3

  18. mathgirl73
    • 2 years ago
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    6/3=2 so you have a^2

  19. mathgirl73
    • 2 years ago
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    now you will have 8^-2/3 a^2

  20. mathgirl73
    • 2 years ago
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    you can't have negative exponents so you drop 8-2/3 down in the denominator and it becomes 8^2/3

  21. mathgirl73
    • 2 years ago
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    now you have a^2/8^2/3

  22. mathgirl73
    • 2 years ago
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    if you havent learned how to convert fractional exponents to radicals then you can stop there

  23. mathgirl73
    • 2 years ago
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    but if not you convert 8 2/3 to a radical

  24. mathgirl73
    • 2 years ago
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    |dw:1354927080454:dw|

  25. xKingx
    • 2 years ago
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    I think I get it lol

  26. mathgirl73
    • 2 years ago
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    ok

  27. geoffb
    • 2 years ago
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    "you can't have negative exponents" Sure you can. The rest of what you said looks good though.

  28. mathgirl73
    • 2 years ago
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    you can but 99.9% of the time n Algebra, teachers want the answer using positive exponents.

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