Multiply $ \dfrac{10x^3y^4}{15x} $ by $ 3 $ to get $ \dfrac{ 30x^3y^4 }{ 15x } $.

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.

$$ \begin{aligned} \frac{10x^3y^4}{15x} \cdot 3 & \xlongequal{\text{Step 1}} \frac{10x^3y^4}{15x} \cdot \frac{3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 10x^3y^4 \cdot 3 }{ 15x \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 30x^3y^4 }{ 15x } \end{aligned} $$

Multiply $ \dfrac{30x^3y^4}{15x} $ by $ x $ to get $ \dfrac{ 30x^4y^4 }{ 15x } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{30x^3y^4}{15x} \cdot x & \xlongequal{\text{Step 1}} \frac{30x^3y^4}{15x} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 30x^3y^4 \cdot x }{ 15x \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 30x^4y^4 }{ 15x } \end{aligned} $$

Multiply $ \dfrac{30x^4y^4}{15x} $ by $ \dfrac{y}{6y^4} $ to get $ \dfrac{ 30x^4y^5 }{ 90xy^4 } $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{30x^4y^4}{15x} \cdot \frac{y}{6y^4} & \xlongequal{\text{Step 1}} \frac{ 30x^4y^4 \cdot y }{ 15x \cdot 6y^4 } \xlongequal{\text{Step 2}} \frac{ 30x^4y^5 }{ 90xy^4 } \end{aligned} $$