Question

(\frac{(2x^{5})^{-3}}{x^{4}})

Explanation:

Step1: Simplify the numerator's exponent

Apply power rule: $(ab)^n=a^n b^n$ and $(x^m)^n=x^{m \cdot n}$
$$(2x^5)^{-3}=2^{-3} \cdot (x^5)^{-3}=\frac{1}{8}x^{-15}=\frac{1}{8x^{15}}$$

Step2: Rewrite division as multiplication

Divide by $x^4$ is multiply by $\frac{1}{x^4}$
$$\frac{1}{8x^{15}} \cdot \frac{1}{x^4}$$

Step3: Combine like terms

Use exponent rule: $x^m \cdot x^n=x^{m+n}$
$$\frac{1}{8x^{15+4}}=\frac{1}{8x^{19}}$$

Answer:

$\frac{1}{8x^{19}}$