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Simplify the expression

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

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Erica M. | Tutor for: Math, Science, SAT, Programs: iMovie, FinalCut, AdobeTutor for: Math, Science, SAT, Programs:...
4.9 4.9 (22 lesson ratings) (22)
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Exponents multiply when they are outside of parenthesis (Example: (x^4)^3=x^12) and add when they are on the same variable being multiplied (Example: (x^4)(x^3)=(x^7). 
In this case, the -4 outside of the parenthesis multiplies to both the numerator and the denominator. Careful to pay attention to both numbers on the top though! The -4 applies to the 3 and the x^-4 separately. After multiplying that through, you have:
A negative exponent becomes positive when you switch the number to the other side of the fraction (numerator to denominator or vice versa). Let's do that with the 3^-4. 
Now multiply out the 3^4 to get the final answer:


Just wonder, according to what any tutor can get a check of  "Best answer"?
Sameer A. | Senior VB.NET Programmer (Web/Windows)Senior VB.NET Programmer (Web/Windows)
5.0 5.0 (2 lesson ratings) (2)
(3x^-4/y^-3)^-4 = (3y^3/x^4)^-4
(3y^3/x^4)^-4 = (x^4/3y^3)^4
(x^4/3y^3)^4 = (x^4)^4/(3^4)*(y^3)^4
(x^4)^4/(3^4)*(y^3)^4 = (x^16)/81(y^12)