Simplify the expression

Question

Simplify 

 

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

Answer 1

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)

Answer 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)