Multiply $90$ by $ \dfrac{x^5}{15} $ to get $ \dfrac{ 90x^5 }{ 15 } $.

Step 1: Write $ 90 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 90 \cdot \frac{x^5}{15} & \xlongequal{\text{Step 1}} \frac{90}{\color{red}{1}} \cdot \frac{x^5}{15} \xlongequal{\text{Step 2}} \frac{ 90 \cdot x^5 }{ 1 \cdot 15 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 90x^5 }{ 15 } \end{aligned} $$

Multiply $ \dfrac{90x^5}{15} $ by $ x^5 $ to get $ \dfrac{ 90x^{10} }{ 15 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{90x^5}{15} \cdot x^5 & \xlongequal{\text{Step 1}} \frac{90x^5}{15} \cdot \frac{x^5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 90x^5 \cdot x^5 }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 90x^{10} }{ 15 } \end{aligned} $$

Add $-18x^4$ and $ \dfrac{90x^{10}}{15} $ to get $ \dfrac{ \color{purple}{ 90x^{10}-270x^4 } }{ 15 }$.

Step 1: Write $ -18x^4 $ 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 first fraction by $\color{blue}{ 15 }$.

$$ \begin{aligned} -18x^4+ \frac{90x^{10}}{15} & \xlongequal{\text{Step 1}} \frac{-18x^4}{\color{red}{1}} + \frac{90x^{10}}{15} = \frac{ \left( -18x^4 \right) \cdot \color{blue}{ 15 }}{ 1 \cdot \color{blue}{ 15 }} + \frac{ 90x^{10} }{ 15 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -270x^4 } }{ 15 } + \frac{ \color{purple}{ 90x^{10} } }{ 15 }=\frac{ \color{purple}{ 90x^{10}-270x^4 } }{ 15 } \end{aligned} $$