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(x^4y^3)^(-2)/(x^3y^2)^(-4) =

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(x^4y^3)^(-2)/(x^3y^2)^(-4) =  [#permalink]

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New post 04 Apr 2018, 23:40
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

86% (01:03) correct 14% (01:40) wrong based on 100 sessions

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Re: (x^4y^3)^(-2)/(x^3y^2)^(-4) =  [#permalink]

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New post 04 Apr 2018, 23:54
Bunuel wrote:
\(\frac{(x^4y^3)^{(-2)}}{(x^3y^2)^{(-4)}}=\)


A. \(x^{-4}y^{-2}\)

B. \(xy\)

C. \(x^3y^3\)

D. \(x^2y^2\)

E. \(x^4y^2\)


we know that if we have negative inverse sign we can easily avoid it changing their numerator and denominator position.

(x^3. y^2)^4/(x^4. y^3)^2

=x^12. y^8 / x^8. y^6
=x^4.y^2

which is option E.
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Re: (x^4y^3)^(-2)/(x^3y^2)^(-4) =  [#permalink]

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New post 05 Apr 2018, 12:17
Bunuel wrote:
\(\frac{(x^4y^3)^{(-2)}}{(x^3y^2)^{(-4)}}=\)


A. \(x^{-4}y^{-2}\)

B. \(xy\)

C. \(x^3y^3\)

D. \(x^2y^2\)

E. \(x^4y^2\)

Three steps:

\(\frac{(x^4y^3)^{(-2)}}{(x^3y^2)^{(-4)}} = \frac{(x^{-8}y^{-6})}{(x^{-12}y^{-8})}=\)

\(x^{-8-(-12)}y^{-6-(-8)} = x^4y^2\)

Answer E

Simpler steps.
Invert the fraction, change exponents' signs*

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

Distribute the exponent:\((a^{m})^{n}=a^{m*n}=a^{mn}\)

\(\frac{(x^3y^2)^{(4)}}{(x^4y^3)^{(2)}}=\frac{x^{12}y^8}{x^8y^6}\)

Divide: keep the base, subtract the exponent

\(\frac{x^{12}y^8}{x^8y^6}= x^{(12-8)}y^{(8-6)}= x^4y^2\)

Answer E

*A term with a negative exponent in the numerator or denominator can be moved to the opposite side of the fraction, i.e., to denominator or numerator, respectively. Change the sign of the exponent.
\(\frac{4^{-2}}{2^{-2}}=\frac{(\frac{1}{4^2})}{(\frac{1}{2^2})}=(\frac{1}{4^2}*\frac{2^2}{1})=(\frac{1}{16}*4)=\frac{4}{16}\)

Easier:\(\frac{4^{-2}}{2^{-2}}=\frac{2^2}{4^2}=\frac{4}{16}\)

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Re: (x^4y^3)^(-2)/(x^3y^2)^(-4) =  [#permalink]

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New post 23 Dec 2018, 07:39
We can easily solve this with: (x^a)^b = x^(a*b) and (x^a)/(x^b) = x^(a-b)
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Re: (x^4y^3)^(-2)/(x^3y^2)^(-4) =  [#permalink]

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New post 23 Dec 2018, 08:19
Bunuel wrote:
\(\frac{(x^4y^3)^{(-2)}}{(x^3y^2)^{(-4)}}=\)


A. \(x^{-4}y^{-2}\)

B. \(xy\)

C. \(x^3y^3\)

D. \(x^2y^2\)

E. \(x^4y^2\)


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

= \(\frac{(x^{-8}y^{-6})}{(x^{-12}y^{-8})}\)

= \((x^{-8 + 12}y^{-6 + 8})\)

= \(x^4y^2\), Answer must be (E)
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Re: (x^4y^3)^(-2)/(x^3y^2)^(-4) =   [#permalink] 23 Dec 2018, 08:19
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