The problem is to simplify the expression $(\frac{8xy^{-1}}{y^5})^{-2}$ and express the answer with positive exponents.

1. Problem Description

The problem is to simplify the expression $(\frac{8xy^{-1}}{y^5})^{-2}$ and express the answer with positive exponents.

2. Solution Steps

We have $(\frac{8xy^{-1}}{y^5})^{-2}$.

First, we simplify the expression inside the parentheses:

$\frac{8xy^{-1}}{y^5} = 8xy^{-1}y^{-5} = 8xy^{-1-5} = 8xy^{-6}$

Now, we raise this to the power of $-2$:

$(8xy^{-6})^{-2} = 8^{-2}x^{-2}(y^{-6})^{-2} = 8^{-2}x^{-2}y^{(-6)(-2)} = 8^{-2}x^{-2}y^{12}$

Now, we convert the negative exponents to positive exponents:

$8^{-2}x^{-2}y^{12} = \frac{1}{8^2} \cdot \frac{1}{x^2} \cdot y^{12} = \frac{y^{12}}{8^2x^2} = \frac{y^{12}}{64x^2}$

$a^{-n} = \frac{1}{a^n}$

$(a^m)^n = a^{mn}$

3. Final Answer

$\frac{y^{12}}{64x^2}$