Multiply $x^7$ by $ \dfrac{y^8}{x^5y^6-x^{10}y^5} $ to get $ \dfrac{x^7y^8}{-x^{10}y^5+x^5y^6} $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} x^7 \cdot \frac{y^8}{x^5y^6-x^{10}y^5} & \xlongequal{\text{Step 1}} \frac{x^7}{\color{red}{1}} \cdot \frac{y^8}{x^5y^6-x^{10}y^5} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ x^7 \cdot y^8 }{ 1 \cdot \left( x^5y^6-x^{10}y^5 \right) } \xlongequal{\text{Step 3}} \frac{ x^7y^8 }{ x^5y^6-x^{10}y^5 } = \\[1ex] &= \frac{x^7y^8}{-x^{10}y^5+x^5y^6} \end{aligned} $$