Multiply $ \dfrac{7}{18} $ by $ x^4 $ to get $ \dfrac{ 7x^4 }{ 18 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{7}{18} \cdot x^4 & \xlongequal{\text{Step 1}} \frac{7}{18} \cdot \frac{x^4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7 \cdot x^4 }{ 18 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x^4 }{ 18 } \end{aligned} $$

Multiply $ \dfrac{2}{27} $ by $ x^3 $ to get $ \dfrac{ 2x^3 }{ 27 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{2}{27} \cdot x^3 & \xlongequal{\text{Step 1}} \frac{2}{27} \cdot \frac{x^3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2 \cdot x^3 }{ 27 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^3 }{ 27 } \end{aligned} $$

Multiply $ \dfrac{7x^4}{18} $ by $ y $ to get $ \dfrac{ 7x^4y }{ 18 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{7x^4}{18} \cdot y & \xlongequal{\text{Step 1}} \frac{7x^4}{18} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7x^4 \cdot y }{ 18 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x^4y }{ 18 } \end{aligned} $$

Multiply $ \dfrac{2x^3}{27} $ by $ y^2 $ to get $ \dfrac{ 2x^3y^2 }{ 27 } $.

Step 1: Write $ y^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{2x^3}{27} \cdot y^2 & \xlongequal{\text{Step 1}} \frac{2x^3}{27} \cdot \frac{y^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2x^3 \cdot y^2 }{ 27 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^3y^2 }{ 27 } \end{aligned} $$

Multiply $ \dfrac{7x^4}{18} $ by $ y $ to get $ \dfrac{ 7x^4y }{ 18 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{7x^4}{18} \cdot y & \xlongequal{\text{Step 1}} \frac{7x^4}{18} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7x^4 \cdot y }{ 18 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x^4y }{ 18 } \end{aligned} $$

Multiply $ \dfrac{2x^3y^2}{27} $ by $ a $ to get $ \dfrac{ 2ax^3y^2 }{ 27 } $.

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.

$$ \begin{aligned} \frac{2x^3y^2}{27} \cdot a & \xlongequal{\text{Step 1}} \frac{2x^3y^2}{27} \cdot \frac{a}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2x^3y^2 \cdot a }{ 27 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2ax^3y^2 }{ 27 } \end{aligned} $$

Add $ \dfrac{7x^4y}{18} $ and $ \dfrac{2ax^3y^2}{27} $ to get $ \dfrac{ \color{purple}{ 4ax^3y^2+21x^4y } }{ 54 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 3 }$ and the second by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{7x^4y}{18} + \frac{2ax^3y^2}{27} & = \frac{ 7x^4y \cdot \color{blue}{ 3 }}{ 18 \cdot \color{blue}{ 3 }} + \frac{ 2ax^3y^2 \cdot \color{blue}{ 2 }}{ 27 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 21x^4y } }{ 54 } + \frac{ \color{purple}{ 4ax^3y^2 } }{ 54 }=\frac{ \color{purple}{ 4ax^3y^2+21x^4y } }{ 54 } \end{aligned} $$