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What is (2x⁴y⁻³)⁻¹?

 Jan 23, 2016

Best Answer 

 #1
avatar
+9

Simplify the following:
1/((2 x^4)/y^3)

Multiply the numerator of 1/((2 x^4)/y^3) by the reciprocal of the denominator. 1/((2 x^4)/y^3) = (1 y^3)/(2 x^4):
Answer: | y^3 / (2x^4)

 Jan 23, 2016
 #1
avatar
+9
Best Answer

Simplify the following:
1/((2 x^4)/y^3)

Multiply the numerator of 1/((2 x^4)/y^3) by the reciprocal of the denominator. 1/((2 x^4)/y^3) = (1 y^3)/(2 x^4):
Answer: | y^3 / (2x^4)

Guest Jan 23, 2016
 #2
avatar+8613 
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Great Job Sir/Mam! (:

 Jan 23, 2016
 #3
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+5

First start with    2x^4 y^-3     this equals    (2x^4) / y^3    now invert them due to the - 1 power

y^3/(2x^4)

 Jan 23, 2016
 #4
avatar+8613 
0

#3. Shorter way of doing it. :D. Shorter = better?

Sorry, I seem to be a bit hyper.

 Jan 23, 2016
 #5
avatar+105509 
0

Hi Quazw...

What is (2x⁴y⁻³)⁻¹?

 

This is the easiest way.

 

1) write it as a fraction

 

\(\frac{(2x^4y^{-3})^{-1}}{1}\)

 

2)  Anything that is raised to a negative number gets swapped to the other side of the fraction line and the negaive becomes positive.

[NOTE: negative numbers (coefficients) are NOT negative indices but there are no negative numbers here so I don't need to worry.]

 

\(=\frac{1}{1*(2x^4y^{-3})^{+1}} \qquad \mbox{There was nothing left on the top so I put a 1 there!}\\~\\ =\frac{1}{2x^4y^{-3}} \\~\\ =\frac{y^{+3}}{2x^4} \\~\\ =\frac{y^{3}}{2x^4} \\~\\ \)

.
 Jan 24, 2016

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