Simplaify This 2x^-4y^-3(7x^3y^-2) PLEASE HELP ME

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Simplaify This 2x^-4y^-3(7x^3y^-2) PLEASE HELP ME

Mathematics
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I dont understnad how???
|dw:1327615451961:dw|
a negative index = 1 / positive eg x^-2 = 1/x^2

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the answer can also be written as 14x^-1 y^-5 ( x^-1 = 1/x)
I still doont understanr
hmm - my time is limited at moment - try the khanacademy site wahe - its got a good reputation
why is the 14 positive its -2 x 7 = -14
\[ 2x^{-4}y^{-3}(7x^3y^{-2}) \] this is your expression?
the 7 is negavive
\[ 2x^{-4}y^{-3}(-7x^3y^{-2}) \] is this it?
can u help me do this one \[4a^7b^5m^10(ten) (8a^9-b^-5m^2)+4a^7m^12/(2a^3bm^2)^5\]
wait. Do you have the answer to your first question or not?
yea i just forgot to put the - sigh but i dont get the way jimmy drew it why was the 14 over the other things|dw:1327617362311:dw|
Let's try it one more time. Your question then is: Simply this expression \[ 2x^{-4}y^{-3}(7x^3y^{-2}) \] correct?
the 2 is negative ---the first one
What do we do now?
So it's this: \[ -2x^{-4}y^{-3}(7x^3y^{-2}) \] yes or no?
yes
Right. First of all then, do you agree by the commutative property of multiplication, that we can reorder all of the terms and that \[ -2x^{-4}y^{-3}(7x^3y^{-2}) = (-2)7.x^{-4}x^3.y^{-3}y^{-2} \]
Yes
Good. Now we need to simplify each set of terms appropriately. (-2)7 = -14 that's straight forward I hope. What about \[ x^{-4}x^3 \] what's that equal to?
x\[x-1???\]
x^-1
yes. And \[ y^{-3}y^{-2} \] is equal to what?
y^-5
Yes, hence the answer is \[-14x^{-1}y^{-5} \] which we can also write as \[ \frac{-14}{xy^5} \] that make sense?
I dont get the bottom part
By definition \[ x^{-1} \] means and is equal to \[ \frac{1}{x} \]
Oh
Therefore also \[ y^{-5} = (y^5)^{-1} = \frac{1}{y^5} \]
SO if it has a power of -2 then the numerator is also 2???
in the denominator, yes. For instance \[ 3^{-2} = \frac{1}{3^2} \] That makes good sense because, for example it makes this consistent: \[ 3 = 3^1 \] \[= 3^{3-2} \] \[ = 3^3.3^{-2} \] \[ = 3^3 \frac{1}{3^2} \] \[= 27 \frac{1}{9} \]
k
that last expression is 27 times 1/9 which is of course equal to 3.
Therefore \[ -14x^{-1}y^{-5} = - \frac{14}{xy^5} \]
Thankyou spoooooo much
4a7b5m10(ten)(8a9−b−5m2)+4a7m12/(2a3bm2)5 can u help me with tis one
\[4a7b5m10(ten)(8a9−b−5m2)+4a7m12/(2a3bm2)5\]
ok. good luck with your next one. Work it out patiently. Check it. Do it again. Iron out the errors. See if you can't figure it out. What's you've written is unreadable to me.
oh ill write it again
\[4a^7b^5m^10(ten)(8a^9-b^-5m^2)+4a^7m^12)))divide by (2a^3bm^2)\]
To get more than one thing in the exponent, use curly brackets. For example x^{10} \[ x^{10} \] To write a fraction, use \frac{a}{b} \[ \frac{a}{b} \]

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