55. $$ \left(-\frac{2}{x^{3}}\right)^{5} $$

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To simplify the expression $$ \left(-\frac{2}{x^{3}}\right)^{5} $$, follow these steps:

1. **Raise the numerator and the denominator to the 5th power separately:**

$$
   \left(-\frac{2}{x^{3}}\right)^{5} = \frac{(-2)^5}{(x^{3})^5}
   $$

2. **Calculate $$ (-2)^5 $$ and $$ (x^{3})^5 $$:**

- $$ (-2)^5 = -32 $$ (because a negative number raised to an odd power remains negative)
   - $$ (x^{3})^5 = x^{15} $$ (using the power of a power rule $$ (a^m)^n = a^{m \times n} $$)

3. **Combine the results:**

$$
   \frac{(-2)^5}{(x^{3})^5} = \frac{-32}{x^{15}}
   $$

**Final Simplified Form:**

$$
\boxed{\, -\dfrac{32}{\,x^{15}\,} \,}
$$
$$ -\frac{32}{x^{15}} $$

55. \( \left(-\frac{2}{x^{3}}\right)^{5} \)

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