$$ \left( -2ab^2 \right)^3 = (-2)^3a^3 \left( b^2 \right)^3 = -8a^3b^6 $$

Multiply $ \dfrac{-8a^3b^6}{20} $ by $ a $ to get $ \dfrac{ -8a^4b^6 }{ 20 } $.

Step 1: Write $ a $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-8a^3b^6}{20} \cdot a & \xlongequal{\text{Step 1}} \frac{-8a^3b^6}{20} \cdot \frac{a}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -8a^3b^6 \right) \cdot a }{ 20 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -8a^4b^6 }{ 20 } \end{aligned} $$

Multiply $ \dfrac{-8a^4b^6}{20} $ by $ b^4 $ to get $ \dfrac{ -8a^4b^{10} }{ 20 } $.

Step 1: Write $ b^4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-8a^4b^6}{20} \cdot b^4 & \xlongequal{\text{Step 1}} \frac{-8a^4b^6}{20} \cdot \frac{b^4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -8a^4b^6 \right) \cdot b^4 }{ 20 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -8a^4b^{10} }{ 20 } \end{aligned} $$