use laws of exponents to simplify

Question

(x^-1/4y²)⁴

Answer 1

with exponents it works as follows...

 

 

(3*4) ⁶ = 3⁶*4⁶            distribute exponents to numbers in parenthesis

 

(2²)⁵ = 2^(2*5)              multiply exponents when there are exponents parenthesis

 

2^-5 * 3³ = 3³ /(2⁵)    negative exponent is the same as positive reciprocal

 

 

(x^-1/4y²)⁴

 

Do the steps in that order...

1) distribute the 4 to the x and y terms

2) multiply the exponent that is being distributed

3) put the negative power in the denominator as a positive power

Answer 2

(x^ay^b)^c = x^acy^bc

 

In your problem, a = -1/4, b = 2, c = 4.  Plug them in and see what you get.