$$14x^4 \cdot \dfrac{y}{2}x^3y^5=\dfrac{14x^7y^6}{2}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}14x^4\frac{y}{2}x^3y^5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{14x^4y}{2}x^3y^5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{14x^7y}{2}y^5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{14x^7y^6}{2}\end{aligned} $$ | |
| ① | Multiply $14x^4$ by $ \dfrac{y}{2} $ to get $ \dfrac{ 14x^4y }{ 2 } $. Step 1: Write $ 14x^4 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 14x^4 \cdot \frac{y}{2} & \xlongequal{\text{Step 1}} \frac{14x^4}{\color{red}{1}} \cdot \frac{y}{2} \xlongequal{\text{Step 2}} \frac{ 14x^4 \cdot y }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 14x^4y }{ 2 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{14x^4y}{2} $ by $ x^3 $ to get $ \dfrac{ 14x^7y }{ 2 } $. Step 1: Write $ x^3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{14x^4y}{2} \cdot x^3 & \xlongequal{\text{Step 1}} \frac{14x^4y}{2} \cdot \frac{x^3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 14x^4y \cdot x^3 }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 14x^7y }{ 2 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{14x^7y}{2} $ by $ y^5 $ to get $ \dfrac{ 14x^7y^6 }{ 2 } $. Step 1: Write $ y^5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{14x^7y}{2} \cdot y^5 & \xlongequal{\text{Step 1}} \frac{14x^7y}{2} \cdot \frac{y^5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 14x^7y \cdot y^5 }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 14x^7y^6 }{ 2 } \end{aligned} $$ |