$$20x^6y^4xx^2 \cdot \dfrac{y^3}{4}x^5y^2=\dfrac{20x^{14}y^9}{4}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}20x^6y^4xx^2\frac{y^3}{4}x^5y^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}20x^9y^4\frac{y^3}{4}x^5y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{20x^9y^7}{4}x^5y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{20x^{14}y^7}{4}y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{20x^{14}y^9}{4}\end{aligned} $$ | |
| ① | $$ 20 x^6 y^4 x x^2 = 20 x^{6 + 1 + 2} y^{4} = 20 x^9 y^4 $$ |
| ② | Multiply $20x^9y^4$ by $ \dfrac{y^3}{4} $ to get $ \dfrac{ 20x^9y^7 }{ 4 } $. Step 1: Write $ 20x^9y^4 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 20x^9y^4 \cdot \frac{y^3}{4} & \xlongequal{\text{Step 1}} \frac{20x^9y^4}{\color{red}{1}} \cdot \frac{y^3}{4} \xlongequal{\text{Step 2}} \frac{ 20x^9y^4 \cdot y^3 }{ 1 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 20x^9y^7 }{ 4 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{20x^9y^7}{4} $ by $ x^5 $ to get $ \dfrac{ 20x^{14}y^7 }{ 4 } $. 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. $$ \begin{aligned} \frac{20x^9y^7}{4} \cdot x^5 & \xlongequal{\text{Step 1}} \frac{20x^9y^7}{4} \cdot \frac{x^5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 20x^9y^7 \cdot x^5 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 20x^{14}y^7 }{ 4 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{20x^{14}y^7}{4} $ by $ y^2 $ to get $ \dfrac{ 20x^{14}y^9 }{ 4 } $. Step 1: Write $ y^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{20x^{14}y^7}{4} \cdot y^2 & \xlongequal{\text{Step 1}} \frac{20x^{14}y^7}{4} \cdot \frac{y^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 20x^{14}y^7 \cdot y^2 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 20x^{14}y^9 }{ 4 } \end{aligned} $$ |