Multiply $ \dfrac{16xy^3}{2} $ by $ x $ to get $ \dfrac{ 16x^2y^3 }{ 2 } $.

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.

$$ \begin{aligned} \frac{16xy^3}{2} \cdot x & \xlongequal{\text{Step 1}} \frac{16xy^3}{2} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 16xy^3 \cdot x }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 16x^2y^3 }{ 2 } \end{aligned} $$

Add $ \dfrac{16x^2y^3}{2} $ and $ 5y^7 $ to get $ \dfrac{ \color{purple}{ 10y^7+16x^2y^3 } }{ 2 }$.

Step 1: Write $ 5y^7 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

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

$$ \begin{aligned} \frac{16x^2y^3}{2} +5y^7 & \xlongequal{\text{Step 1}} \frac{16x^2y^3}{2} + \frac{5y^7}{\color{red}{1}} = \frac{ 16x^2y^3 }{ 2 } + \frac{ 5y^7 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 16x^2y^3 } }{ 2 } + \frac{ \color{purple}{ 10y^7 } }{ 2 }=\frac{ \color{purple}{ 10y^7+16x^2y^3 } }{ 2 } \end{aligned} $$