#### Answer

$-\frac{1}{4}$

#### Work Step by Step

Step 1: $(-64)^{-\frac{1}{3}}$
Step 2: $(-4^{3})^{-\frac{1}{3}}$
Step 3: $(-1\times4^{3})^{-\frac{1}{3}}$
Step 4: $(-1^{-\frac{1}{3}}\times4^{3\times-\frac{1}{3}})$
Step 5: Simplifying $-1^{-\frac{1}{3}}$
$-1^{-\frac{1}{3}}=-1$
Step 6: Simplifying exponential powers on 4,
$3\times-\frac{1}{3}=-1$
Step 7: Now the expression becomes $(-1\times4^{-1})$ or $(-1\times\frac{1}{4})$
Step 8: This is simplified to $-\frac{1}{4}$