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



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jim_thompson5910
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what does (z)^3 simplify to

greeneyes<3
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1
z?
I don't know... :/


jim_thompson5910
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(z)^3 = (1*z)^3
(z)^3 = (1)^3*(z)^3
(z)^3 = 1*z^3
(z)^3 = z^3

jim_thompson5910
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(z)^3(3z^4)
turns into
z^3*3z^4

jim_thompson5910
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2
what's next?

greeneyes<3
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1
add the z's but the negative is still messing me up :/

jim_thompson5910
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2
think of
z^3*3z^4
as
1z^3*3z^4

jim_thompson5910
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2
so the coefficients are 1 and 3, they multiply to 1*3 = 3

jim_thompson5910
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2
z^3 times z^4 = z^(3+4) = z^7
so the final answer is 3z^7

greeneyes<3
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thank you! :)
can you help me with the second one as well?

jim_thompson5910
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how far did you get with it?

greeneyes<3
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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)?

jim_thompson5910
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2
the exponent of 3 only applies to terms inside the parenthesis

jim_thompson5910
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so (x^2z^6)^3 means you cube x^2 and z^6

greeneyes<3
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I got 1/25 after simplifying

jim_thompson5910
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let me check

jim_thompson5910
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you are correct

greeneyes<3
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thank you for helping me! :) you're the best! :)

jim_thompson5910
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you're welcome