Multiply $8v^4$ by $ \dfrac{x^5}{16} $ to get $ \dfrac{ 8v^4x^5 }{ 16 } $.

Step 1: Write $ 8v^4 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 8v^4 \cdot \frac{x^5}{16} & \xlongequal{\text{Step 1}} \frac{8v^4}{\color{red}{1}} \cdot \frac{x^5}{16} \xlongequal{\text{Step 2}} \frac{ 8v^4 \cdot x^5 }{ 1 \cdot 16 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8v^4x^5 }{ 16 } \end{aligned} $$

Multiply $ \dfrac{8v^4x^5}{16} $ by $ w^6 $ to get $ \dfrac{ 8v^4w^6x^5 }{ 16 } $.

Step 1: Write $ w^6 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{8v^4x^5}{16} \cdot w^6 & \xlongequal{\text{Step 1}} \frac{8v^4x^5}{16} \cdot \frac{w^6}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 8v^4x^5 \cdot w^6 }{ 16 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8v^4w^6x^5 }{ 16 } \end{aligned} $$

Multiply $ \dfrac{8v^4w^6x^5}{16} $ by $ x^2 $ to get $ \dfrac{ 8v^4w^6x^7 }{ 16 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{8v^4w^6x^5}{16} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{8v^4w^6x^5}{16} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 8v^4w^6x^5 \cdot x^2 }{ 16 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8v^4w^6x^7 }{ 16 } \end{aligned} $$

Add $ \dfrac{8v^4w^6x^7}{16} $ and $ 12x^5 $ to get $ \dfrac{ \color{purple}{ 8v^4w^6x^7+192x^5 } }{ 16 }$.

Step 1: Write $ 12x^5 $ 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 $\color{blue}{16}$.

$$ \begin{aligned} \frac{8v^4w^6x^7}{16} +12x^5 & \xlongequal{\text{Step 1}} \frac{8v^4w^6x^7}{16} + \frac{12x^5}{\color{red}{1}} = \frac{ 8v^4w^6x^7 }{ 16 } + \frac{ 12x^5 \cdot \color{blue}{ 16 }}{ 1 \cdot \color{blue}{ 16 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 8v^4w^6x^7 } }{ 16 } + \frac{ \color{purple}{ 192x^5 } }{ 16 }=\frac{ \color{purple}{ 8v^4w^6x^7+192x^5 } }{ 16 } \end{aligned} $$