HatSimulator
A rectangular pasture has a fence around the perimeter. The length of the fence is 16x7 and the width is 48x4. What is the area of the pasture? (1 point)
a) 3x^3
b)128x^11
c)768x^11
d)768x^28
I KNOW the answer is c, but i need it explained. I already found it here once but can ANYONE explain how to do this?
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hartnn
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Area of rectangular (here pasture) = Length * Width
HatSimulator
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Allright, so how do i do it? 16 * ^7 gives nothing and im so confused
How do i do 16x^7 * 48x^4?
I dont get this problem
HatSimulator
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Same thing with this > Simplify. 5^–1(3^–2)
If i type this into a calculator i get a stupid number
hartnn
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ok, treat constants and variables separately.
\(16x^7 \times 48x^4 = (16\times 48) \times(x^7 \times x^4)\)
got this ?
HatSimulator
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Okay... yes i think i get that... but where did the two Z come from
hartnn
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Z ?? there are no Z's there....
HatSimulator
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Whoops, sorry, okay, go on. I understand now
HatSimulator
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I think i get it
16 * 48 = 768
And 7 + 4 = 11?
hartnn
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good!
HatSimulator
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Okay, 1 more?
hartnn
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actually, its \(x^7 \times x^4 = x^{7+4}=x^{11}\)
and sure :)
HatSimulator
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Okay
something like this
Simplify (4xy2)3(xy)5
and (sorry) this
Evaluate a–4b2 for a = –2 and b = 4
HatSimulator
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Simplify (4xy^2)^3(xy)^5
Sorry
hartnn
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i believe the first one looks like this :
\((4xy^2)^3(xy)^5\)
hartnn
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ok, so you need to remember/understand few thing before u start:
\(\huge (ab)^n = a^nb^n\)
and
\(\huge (a^m)^n=a^{mn}\)
HatSimulator
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okay
HatSimulator
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The other problem i can't figure out how to write an equation
hartnn
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\(\large Evaluate \: \: a^{–4}b^2 \:\: for\:\: a = –2 \:\:and\:\: b = 4\)
right ?
HatSimulator
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Here you go
hartnn
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ok, for the previous one :
using, \(\huge (ab)^n = a^nb^n\)
\(\large (4xy^2)^3= 4^3 x^3 (y^2)^3\)
got this ?
HatSimulator
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Oh man. So confused
HatSimulator
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Are you doing Simplify (4xy^2)^3(xy)^5 ?
hartnn
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yes.
HatSimulator
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And you changed that to (4xy^2)^3=4^3x^3(y^2)^3....
HatSimulator
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How did you do that... that hurts my brain
hartnn
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|dw:1360891677558:dw|
hartnn
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open up your brain and try to accept new things :)
hartnn
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basically the exponent outside the bracket becomes the exponent of each of the terms inside the bracket.
HatSimulator
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Where did averything after that equal sign come from? Where'd the 5 go?
HatSimulator
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Howd 4 and the 4 more exponents come from
hartnn
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(4xy^2)^3(xy)^5 <------you are asking about this 5 ?
i am starting with (4xy^2)^3 part of (4xy^2)^3(xy)^5
hartnn
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if you are asking from where does all the exponents come from take a look at this again :
\((ab)^n=a^nb^n\)
or perhaps :
\((abc)^n=a^nb^nc^n\)
HatSimulator
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OHHHHHHHHHHHHHHHHHH
HatSimulator
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Yes, yes, go on (:
hartnn
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so i assume you are clear with this diagram.|dw:1360892207194:dw|
using same rule, can you tell me what u get for
\((xy)^5\)
??
HatSimulator
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|dw:1360892393038:dw|
hartnn
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correct :) see, it isn't difficult at all.
now you have
\(\large 4^3x^3(y^2)^3x^5y^5\)
right ?
lets start simplifying with constants (numbers)
4^3 =... ?
HatSimulator
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64
hartnn
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yes.
now comes the 2nd rule i posted.
\(\huge (a^m)^n=a^{mn}\)
so, what about \((y^2)^3\) ??
HatSimulator
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|dw:1360892627948:dw|
hartnn
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12? how ?
HatSimulator
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Wait
HatSimulator
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|dw:1360892663950:dw|
HatSimulator
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y^1*2
hartnn
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umm..no, let me give you an example
\(\large (z^5)^3 = z^{5 \times 3 }=z^{15}\)
do similar thing for \((y^2)^3 \)
HatSimulator
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(y^2)
hartnn
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:O
the exponents are getting multiplied.
what are the 2 exponents in \((y^2)^3\)
HatSimulator
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Its a 3 isnt it... Sorry
(y^6)
hartnn
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yes, y^6 is correct.
so, we have now
\(64x^3y^6x^5y^5\)
lets bring 'x' terms and y terms together.
hartnn
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\(64 \: \: (x^3x^5) \:\: (y^6y^5)\)
ok, any doubts ?
HatSimulator
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No, i got it so far.
hartnn
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now one of the very important rule :
\(\large a^m a^n = a^{m+n}\)
here, if we multiply the variables, their exponents gets ADDED .
so, what about
\(x^3x^5=... ?\)
HatSimulator
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It would end up being 64(x^8)(y^11) ?
HatSimulator
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Thats the answer
hartnn
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wow! thats absolutely correct! :)
hartnn
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did you get how ?
HatSimulator
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Yep!
HatSimulator
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I get it now
HatSimulator
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Thank you very much!
hartnn
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welcome ^_^