How do you simplify fractions with powers?

Question

Like this one:

(3x^2)^2 y^4 / 3y^2 (It'd be easier if you wrote it down on paper)

There's four answers to choose from:

1.) y^2 / 3

2.) x^4 y^2 / 1

3.) 3x^2 y^2

4.) 3x^4 y^2

Please explain why! I completely don't get this.

Answer 1

The answer is 4)

The laws of indicies.  Anything powering a powered number is the samething as adding that powers, ie;

(3X²)² = 3(X²+²)

       =3X^4

Answer 2

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

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

= 3x^4 y^2

----->4). 3x^4 y^2

Answer 3

Answer 4 is the correct answer.

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

=(9x^4y^4)/(3y^2)

=(9/3)(x^4)((y^4)/(y^2))

=3x^4y^2

Answer 4

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

you can cancel out similar factors from the bottom and the top (3,y^2)

((x^2)^2 y^2)

(x^4y^2)   this is the answer (number 2)

Answer 5

lets start by looking at the numerator of your fraction.

(3x^2)^2 = (3x^2)(3x^2)

             = (9x^4)

so our numerator is (9x^4)(y^4)

so we have (9x^4)(y^4) / (3y^2)

we can simplify the 9 and the 3 and have just a 3 in the numerator.

In addition we can simplify the y^4 over y^2 to just y^2 on top

so we have: (3x^4)(y^2)