Multiply $ \dfrac{4}{9} $ by $ k^5 $ to get $ \dfrac{ 4k^5 }{ 9 } $.

Step 1: Write $ k^5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{4}{9} \cdot k^5 & \xlongequal{\text{Step 1}} \frac{4}{9} \cdot \frac{k^5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4 \cdot k^5 }{ 9 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4k^5 }{ 9 } \end{aligned} $$

Multiply $ \dfrac{4k^5}{9} $ by $ 3 $ to get $ \dfrac{ 12k^5 }{ 9 } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{4k^5}{9} \cdot 3 & \xlongequal{\text{Step 1}} \frac{4k^5}{9} \cdot \frac{3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4k^5 \cdot 3 }{ 9 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12k^5 }{ 9 } \end{aligned} $$

Multiply $ \dfrac{12k^5}{9} $ by $ \dfrac{k^3}{3} $ to get $ \dfrac{ 12k^8 }{ 27 } $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{12k^5}{9} \cdot \frac{k^3}{3} \xlongequal{\text{Step 1}} \frac{ 12k^5 \cdot k^3 }{ 9 \cdot 3 } \xlongequal{\text{Step 2}} \frac{ 12k^8 }{ 27 } \end{aligned} $$