Simplify:

4xy^3/z^2 divided by (8x^2y/z^3)^2

I came up with the following:

2.2.x.y.y.y.z.z.z.z.z/z.z.z2.2.16.x.x.x.x.y.y

Simplified into x^3y/16x^3.

Is this correct?

Thanks for your help earlier and now.

No. x^3*y/16 = y/16, and that is not the answer.

You've got a (1/z^2) divided by a (1/z^6), which should be z^4, yet you have no "z" term in your answer.

Try writing it as
4x*y^3*z^6/(z^2*64*x^4*y^2)
and then canceling terms.

To simplify the given expression 4xy^3/z^2 divided by (8x^2y/z^3)^2, we can follow these steps:

Step 1: Simplify the numerator.
The numerator is 4xy^3/z^2. Since there are no like terms to combine or anything else to simplify, we leave it as is.

Step 2: Simplify the denominator.
The denominator is (8x^2y/z^3)^2. To square this expression, we square each term within the parentheses individually. So, (8x^2y/z^3)^2 becomes (8^2)(x^2)^2(y^2)/(z^3)^2, which simplifies to 64x^4y^2/z^6.

Step 3: Divide the simplified numerator by the simplified denominator.
Dividing the numerator 4xy^3/z^2 by the denominator 64x^4y^2/z^6 is equivalent to multiplying the numerator by the reciprocal of the denominator.

So, we have:
(4xy^3/z^2) ÷ (64x^4y^2/z^6) = (4xy^3/z^2) * (z^6/64x^4y^2)

Simplifying further, we can cancel out some common factors:
= (4xy^3 * z^6) / (z^2 * 64x^4y^2)
= (4 * x * y^3 * z^6) / (64 * x^4 * y^2 * z^2)

Now, we can simplify the expression by dividing the coefficients and subtracting the exponents:
= (1/16) * (y^3/y^2) * (z^6/z^2) * (x/x^4)

The y terms simplify to y^(3-2) = y, the z terms simplify to z^(6-2) = z^4, and the x terms simplify to x^(1-4) = 1/x^3.

Thus, the simplified expression is:
= (1/16) * (y) * (z^4) * (1/x^3)
= yz^4 / (16x^3)

Hence, the correct simplification is yz^4 / (16x^3), and your answer of x^3y/16x^3 is incorrect.