$$10\cdot\dfrac{u^3}{w^2}\dfrac{w}{2}u^2v^2=\dfrac{10u^5v^2w}{2w^2}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}10 \cdot \frac{u^3}{w^2}\frac{w}{2}u^2v^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{10u^3}{w^2}\frac{w}{2}u^2v^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10u^3w}{2w^2}u^2v^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{10u^5w}{2w^2}v^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{10u^5v^2w}{2w^2}\end{aligned} $$ | |
| ① | Multiply $10$ by $ \dfrac{u^3}{w^2} $ to get $ \dfrac{ 10u^3 }{ w^2 } $. Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 10 \cdot \frac{u^3}{w^2} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} \cdot \frac{u^3}{w^2} \xlongequal{\text{Step 2}} \frac{ 10 \cdot u^3 }{ 1 \cdot w^2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10u^3 }{ w^2 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{10u^3}{w^2} $ by $ \dfrac{w}{2} $ to get $ \dfrac{ 10u^3w }{ 2w^2 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{10u^3}{w^2} \cdot \frac{w}{2} & \xlongequal{\text{Step 1}} \frac{ 10u^3 \cdot w }{ w^2 \cdot 2 } \xlongequal{\text{Step 2}} \frac{ 10u^3w }{ 2w^2 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{10u^3w}{2w^2} $ by $ u^2 $ to get $ \dfrac{ 10u^5w }{ 2w^2 } $. Step 1: Write $ u^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{10u^3w}{2w^2} \cdot u^2 & \xlongequal{\text{Step 1}} \frac{10u^3w}{2w^2} \cdot \frac{u^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 10u^3w \cdot u^2 }{ 2w^2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10u^5w }{ 2w^2 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{10u^5w}{2w^2} $ by $ v^2 $ to get $ \dfrac{ 10u^5v^2w }{ 2w^2 } $. Step 1: Write $ v^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{10u^5w}{2w^2} \cdot v^2 & \xlongequal{\text{Step 1}} \frac{10u^5w}{2w^2} \cdot \frac{v^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 10u^5w \cdot v^2 }{ 2w^2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10u^5v^2w }{ 2w^2 } \end{aligned} $$ |