The problem asks to simplify the expression $(w^8x^{-3}y^3)^{-2}$ and express the answer using exponents.

1. Problem Description

The problem asks to simplify the expression $(w^8x^{-3}y^3)^{-2}$ and express the answer using exponents.

2. Solution Steps

To simplify the expression $(w^8x^{-3}y^3)^{-2}$, we need to apply the power of a product rule, which states that $(ab)^n = a^n b^n$. We also need to apply the power of a power rule, which states that $(a^m)^n = a^{m \cdot n}$.

Applying the power of a product rule:

$(w^8x^{-3}y^3)^{-2} = (w^8)^{-2} (x^{-3})^{-2} (y^3)^{-2}$

Applying the power of a power rule to each term:

$(w^8)^{-2} = w^{8 \cdot (-2)} = w^{-16}$

$(x^{-3})^{-2} = x^{-3 \cdot (-2)} = x^6$

$(y^3)^{-2} = y^{3 \cdot (-2)} = y^{-6}$

So we have:

$w^{-16}x^6y^{-6}$

To express the answer using only positive exponents, we can rewrite the terms with negative exponents as fractions.

$w^{-16} = \frac{1}{w^{16}}$

$y^{-6} = \frac{1}{y^6}$

Therefore, we can rewrite the expression as:

$w^{-16}x^6y^{-6} = \frac{1}{w^{16}} \cdot x^6 \cdot \frac{1}{y^6} = \frac{x^6}{w^{16}y^6}$

3. Final Answer

$\frac{x^6}{w^{16}y^6}$