Simplify

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

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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:

((3^-4)(x^16))/(y^12)

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.

(x^16)/((3^4)(y^12))

Now multiply out the 3^4 to get the final answer:

(x^16)/(81y^12)

Sameer A. | Senior VB.NET Programmer (Web/Windows)Senior VB.NET Programmer (Web/Windows)

(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)**

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