anonymous
  • anonymous
Help! Simplify: 1. (-z)^3(3z^4) 2. 5(x^2z^6)^3(5x^2z^6)^-3 Thank you!:)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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jim_thompson5910
  • jim_thompson5910
what does (-z)^3 simplify to
anonymous
  • anonymous
-z? I don't know... :/
jim_thompson5910
  • jim_thompson5910
close

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jim_thompson5910
  • jim_thompson5910
(-z)^3 = (-1*z)^3 (-z)^3 = (-1)^3*(z)^3 (-z)^3 = -1*z^3 (-z)^3 = -z^3
jim_thompson5910
  • jim_thompson5910
(-z)^3(3z^4) turns into -z^3*3z^4
jim_thompson5910
  • jim_thompson5910
what's next?
anonymous
  • anonymous
add the z's but the negative is still messing me up :/
jim_thompson5910
  • jim_thompson5910
think of -z^3*3z^4 as -1z^3*3z^4
jim_thompson5910
  • jim_thompson5910
so the coefficients are -1 and 3, they multiply to -1*3 = -3
jim_thompson5910
  • jim_thompson5910
z^3 times z^4 = z^(3+4) = z^7 so the final answer is -3z^7
anonymous
  • anonymous
thank you! :) can you help me with the second one as well?
jim_thompson5910
  • jim_thompson5910
how far did you get with it?
anonymous
  • anonymous
does exponents distribute first? if so, does the ^3 distribute to the 5 as well or just the (x^2z^6)?
jim_thompson5910
  • jim_thompson5910
the exponent of 3 only applies to terms inside the parenthesis
jim_thompson5910
  • jim_thompson5910
so (x^2z^6)^3 means you cube x^2 and z^6
anonymous
  • anonymous
I got 1/25 after simplifying
jim_thompson5910
  • jim_thompson5910
let me check
jim_thompson5910
  • jim_thompson5910
you are correct
anonymous
  • anonymous
thank you for helping me! :) you're the best! :)
jim_thompson5910
  • jim_thompson5910
you're welcome

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