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anonymous

  • one year ago

FAN, FAN TESTIMONIAL, AND MEDAL!!! PLEASE HELP! Rewrite the rational exponent as a radical expression. 3 to the 2 over 3 power, to the 1 over 6 power the sixth root of 3 the ninth root of 3 the eighteenth root of 3 the sixth root of 3 to the third power I know it's not A.

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  1. BTaylor
    • one year ago
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    So it looks like this? \[\frac{ 3^2 }{ 3^{1/6} }\]

  2. BTaylor
    • one year ago
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    or this? \[\left(3^{2/3}\right)^{1/6}\]

  3. anonymous
    • one year ago
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    Which option is it?

  4. BTaylor
    • one year ago
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    I'm pretty sure the problem is asking about the second one, but it isn't very clear. When you have a number to an exponent, and that quantity to another power, you multiply the two exponents. So, \(\frac{2}{3} \times \frac{1}{6}\)

  5. anonymous
    • one year ago
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    1/9

  6. BTaylor
    • one year ago
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    Exactly. So, that is the ninth root of 3.

  7. anonymous
    • one year ago
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    Thank you! Can you please help me with another one?

  8. BTaylor
    • one year ago
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    sure

  9. anonymous
    • one year ago
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    Explain how the Quotient of Powers was used to simplify this expression. 5 to the fourth power, over 25 = 52 By simplifying 25 to 52 to make both powers base five, and subtracting the exponents By simplifying 25 to 52 to make both powers base five, and adding the exponents By finding the quotient of the bases to be, one fifth and cancelling common factors By finding the quotient of the bases to be, one fifthand simplifying the expression

  10. BTaylor
    • one year ago
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    The first option is correct. \(5^4/5^2 = 5^{4-2} = 5^2 = 25\)

  11. anonymous
    • one year ago
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    Thanks! Sorry, but could you help me with a couple more?

  12. anonymous
    • one year ago
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    Rewrite the rational exponent as a radical by extending the properties of integer exponents. 2 to the 3 over 4 power, all over 2 to the 1 over 2 power the eighth root of 2 to the third power the square root of 2 to the 3 over 4 power the fourth root of 2 the square root of 2

  13. anonymous
    • one year ago
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    @hahagotem plz help i'll fan you too

  14. BTaylor
    • one year ago
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    Since these two exponents are divided, you have \(2^{3/4 - 1/2}\).

  15. anonymous
    • one year ago
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    1/4?

  16. BTaylor
    • one year ago
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    Yes, you get \(2^{1/4}\). When you have a number to a fractional exponent, it is a root. So, \(2^{1/4}\) is the fourth root of 2.

  17. anonymous
    • one year ago
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    So C?

  18. BTaylor
    • one year ago
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    yes

  19. anonymous
    • one year ago
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    I have 1 more can u plz help?

  20. BTaylor
    • one year ago
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    absolutely.

  21. anonymous
    • one year ago
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    A rectangle has a length of the fifth root of 16 inches and a width of 2 to the 1 over 5 power inches. Find the area of the rectangle. 2 to the 3 over 5 power inches squared 2 to the 4 over 5 power inches squared 2 inches squared 2 to the 2 over 5 power inches squared

  22. anonymous
    • one year ago
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    I'm sorry to rush, but I have to get off soon

  23. anonymous
    • one year ago
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    Thanks!

  24. BTaylor
    • one year ago
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    @Jacob902 is correct. \(2^{4/5} \times 2^{1/5} = 2\)

  25. Jacob902
    • one year ago
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    why ?

  26. BTaylor
    • one year ago
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    \(16 = 2^4\), so the fifth root of 16 is \(2^{4/5}\). When you multiply two exponents with the same base, you add the two powers together. \(2^1 = 2\).

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