$$27x^4 \cdot \dfrac{y^5}{12}xy^4=\dfrac{27x^5y^9}{12}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}27x^4\frac{y^5}{12}xy^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{27x^4y^5}{12}xy^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{27x^5y^5}{12}y^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{27x^5y^9}{12}\end{aligned} $$ | |
| ① | Multiply $27x^4$ by $ \dfrac{y^5}{12} $ to get $ \dfrac{ 27x^4y^5 }{ 12 } $. Step 1: Write $ 27x^4 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 27x^4 \cdot \frac{y^5}{12} & \xlongequal{\text{Step 1}} \frac{27x^4}{\color{red}{1}} \cdot \frac{y^5}{12} \xlongequal{\text{Step 2}} \frac{ 27x^4 \cdot y^5 }{ 1 \cdot 12 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 27x^4y^5 }{ 12 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{27x^4y^5}{12} $ by $ x $ to get $ \dfrac{ 27x^5y^5 }{ 12 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{27x^4y^5}{12} \cdot x & \xlongequal{\text{Step 1}} \frac{27x^4y^5}{12} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 27x^4y^5 \cdot x }{ 12 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 27x^5y^5 }{ 12 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{27x^5y^5}{12} $ by $ y^4 $ to get $ \dfrac{ 27x^5y^9 }{ 12 } $. Step 1: Write $ y^4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{27x^5y^5}{12} \cdot y^4 & \xlongequal{\text{Step 1}} \frac{27x^5y^5}{12} \cdot \frac{y^4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 27x^5y^5 \cdot y^4 }{ 12 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 27x^5y^9 }{ 12 } \end{aligned} $$ |