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greeneyes<3

  • 2 years ago

Help! Simplify: 1. (-z)^3(3z^4) 2. 5(x^2z^6)^3(5x^2z^6)^-3 Thank you!:)

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  1. jim_thompson5910
    • 2 years ago
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    what does (-z)^3 simplify to

  2. greeneyes<3
    • 2 years ago
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    -z? I don't know... :/

  3. jim_thompson5910
    • 2 years ago
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    close

  4. jim_thompson5910
    • 2 years ago
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    (-z)^3 = (-1*z)^3 (-z)^3 = (-1)^3*(z)^3 (-z)^3 = -1*z^3 (-z)^3 = -z^3

  5. jim_thompson5910
    • 2 years ago
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    (-z)^3(3z^4) turns into -z^3*3z^4

  6. jim_thompson5910
    • 2 years ago
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    what's next?

  7. greeneyes<3
    • 2 years ago
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    add the z's but the negative is still messing me up :/

  8. jim_thompson5910
    • 2 years ago
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    think of -z^3*3z^4 as -1z^3*3z^4

  9. jim_thompson5910
    • 2 years ago
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    so the coefficients are -1 and 3, they multiply to -1*3 = -3

  10. jim_thompson5910
    • 2 years ago
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    z^3 times z^4 = z^(3+4) = z^7 so the final answer is -3z^7

  11. greeneyes<3
    • 2 years ago
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    thank you! :) can you help me with the second one as well?

  12. jim_thompson5910
    • 2 years ago
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    how far did you get with it?

  13. greeneyes<3
    • 2 years ago
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    does exponents distribute first? if so, does the ^3 distribute to the 5 as well or just the (x^2z^6)?

  14. jim_thompson5910
    • 2 years ago
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    the exponent of 3 only applies to terms inside the parenthesis

  15. jim_thompson5910
    • 2 years ago
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    so (x^2z^6)^3 means you cube x^2 and z^6

  16. greeneyes<3
    • 2 years ago
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    I got 1/25 after simplifying

  17. jim_thompson5910
    • 2 years ago
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    let me check

  18. jim_thompson5910
    • 2 years ago
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    you are correct

  19. greeneyes<3
    • 2 years ago
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    thank you for helping me! :) you're the best! :)

  20. jim_thompson5910
    • 2 years ago
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    you're welcome

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