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HelloKitty17

  • one year ago

If the quantity 4 times x times y cubed plus 8 times x squared times y to the fifth power all over 2 times x times y squared is completely simplified to 2xayb + 4xcyd, where a, b, c, and d represent integer exponents, what is the value of a? _______

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  1. anonymous
    • one year ago
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    Do you have any idea?

  2. mathstudent55
    • one year ago
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    Can you use the equation editor or the draw tool to show what you mean? Is it this? \(\Large \dfrac{4xy^3 + 8x^2y^5}{2xy^2} = 2x^ay^b + x^cy^d\)

  3. HelloKitty17
    • one year ago
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    sort of but the question is asking what is the value of a

  4. OregonDuck
    • one year ago
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    Value of a is zero 2xy2(2y+4xy3)2xy2 cancels the 2xy^2 on top and bottom =2y+4xy3=2x0y1+4x1y3 so x^a= x^0 a=0

  5. mathstudent55
    • one year ago
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    I understand what the question is asking. My question is if the above expression is correct.

  6. mathstudent55
    • one year ago
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    You can separate the left side into two fractions. \(\Large \dfrac{4xy^3 + 8x^2y^5}{2xy^2} = 2x^ay^b + x^cy^d\) \(\Large \dfrac{4xy^3}{2xy^2} + \dfrac{8x^2y^5}{2xy^2} = 2x^ay^b + x^cy^d\) Now reduce each fraction. When you divide powers with the same base, subtract the exponents.

  7. mathstudent55
    • one year ago
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    \(\Large \dfrac{4}{2} \times \dfrac{x}{x} \times \dfrac{y^3}{y^2} + \dfrac{8}{2} \times \dfrac{x^2}{x} \times \dfrac{y^5}{y^2} = 2x^ay^b + x^cy^d\)

  8. mathstudent55
    • one year ago
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    \(\Large 2x^{1-1}y^{3-2} + 4x^{2-1}y^{5-2} = 2x^ay^b + 4x^cy^d\)

  9. mathstudent55
    • one year ago
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    \(\Large 2x^{0}y^{1} + 4x^{1}y^{3} = 2x^ay^b + 4x^cy^d\)

  10. mathstudent55
    • one year ago
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    Now you can compare each exponent on the left side with each variable, a, b, c, and d, on the right side to see what value each of those variables has.

  11. mathstudent55
    • one year ago
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    \(\Large 2x^{\color{red}{0}}y^{\color{green}{1}} + 4x^{\color{blue}{1}}y^{\color{brown}{3}} = 2x^\color{red}{a}y^\color{green}{b} + 4x^\color{blue}{c}y^\color{brown}{d}\)

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