4. $(-2cd^{-3})^2=(-2)^{square}c^{square}d^{square}=square c^{square}square$

Explanation:

Step1: Apply power - of - a - product rule

$(-2cd^{-3})^2=(-2)^2c^2(d^{-3})^2$

Step2: Calculate $(-2)^2$ and apply power - of - a - power rule for $d$

$(-2)^2 = 4$, and $(d^{-3})^2=d^{-3\times2}=d^{-6}$ So the result is $4c^2d^{-6}=\frac{4c^2}{d^{6}}$

Answer:

$(-2)^2c^2d^{-6}$; $4c^2d^{-6}$; $\frac{4c^2}{d^{6}}$