Step 1 :Given the expression \(\left(\frac{a^{3}}{-8 b^{4}}\right)^{2}\)
Step 2 :We can simplify this by applying the power of a power rule, which states that \((a^m)^n = a^{m*n}\).
Step 3 :Applying this rule to each term in the fraction, we get \(\frac{a^{6}}{64 b^{8}}\)
Step 4 :However, since the denominator was negative, the square of it will be positive, so the simplified form of the given expression is \(\boxed{\frac{a^{6}}{64 b^{8}}\)