Answer
$-\frac{1}{64}$
Work Step by Step
Step 1: $-256^{-\frac{3}{4}}$
Step 2: $\frac{1}{(-256)^{\frac{3}{4}}}$
Step 3: Since $4^{4}=256$, the expression becomes $\frac{1}{(-4^{4})^{\frac{3}{4}}}$
Step 4: Simplifying the indexes, the expression becomes $\frac{1}{(-4)^{3}}$
Step 5: This can be simplified as $\frac{1}{-64}$ or $-\frac{1}{64}$
