The problem asks us to simplify the expression $(k^{-3}m^{-8})^8$ and express the answer using exponents.

1. Problem Description

The problem asks us to simplify the expression $(k^{-3}m^{-8})^8$ and express the answer using exponents.

2. Solution Steps

First, we need to apply the power of a power rule: $(a^m)^n = a^{m*n}$. Applying this rule to the given expression, we get:

$(k^{-3}m^{-8})^8 = k^{-3*8}m^{-8*8} = k^{-24}m^{-64}$.

To express the answer using only positive exponents, we need to use the rule $a^{-n} = \frac{1}{a^n}$. Therefore:

$k^{-24}m^{-64} = \frac{1}{k^{24}} \cdot \frac{1}{m^{64}} = \frac{1}{k^{24}m^{64}}$.

3. Final Answer

$\frac{1}{k^{24}m^{64}}$