$$9\cdot\dfrac{x^{16}}{6}{x^2}^3x\cdot2=\dfrac{18x^{23}}{6}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}9 \cdot \frac{x^{16}}{6}{x^2}^3x\cdot2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9 \cdot \frac{x^{16}}{6}\cdot1x^6x\cdot2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{9x^{16}}{6}\cdot1x^6x\cdot2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{9x^{22}}{6}x\cdot2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{9x^{23}}{6}\cdot2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{18x^{23}}{6}\end{aligned} $$ | |
| ① | $$ \left( x^2 \right)^3 = 1^3 \left( x^2 \right)^3 = x^6 $$ |
| ② | Multiply $9$ by $ \dfrac{x^{16}}{6} $ to get $ \dfrac{ 9x^{16} }{ 6 } $. Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 9 \cdot \frac{x^{16}}{6} & \xlongequal{\text{Step 1}} \frac{9}{\color{red}{1}} \cdot \frac{x^{16}}{6} \xlongequal{\text{Step 2}} \frac{ 9 \cdot x^{16} }{ 1 \cdot 6 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9x^{16} }{ 6 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{9x^{16}}{6} $ by $ x^6 $ to get $ \dfrac{ 9x^{22} }{ 6 } $. Step 1: Write $ x^6 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{9x^{16}}{6} \cdot x^6 & \xlongequal{\text{Step 1}} \frac{9x^{16}}{6} \cdot \frac{x^6}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9x^{16} \cdot x^6 }{ 6 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9x^{22} }{ 6 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{9x^{22}}{6} $ by $ x $ to get $ \dfrac{ 9x^{23} }{ 6 } $. 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. $$ \begin{aligned} \frac{9x^{22}}{6} \cdot x & \xlongequal{\text{Step 1}} \frac{9x^{22}}{6} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9x^{22} \cdot x }{ 6 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9x^{23} }{ 6 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{9x^{23}}{6} $ by $ 2 $ to get $ \dfrac{ 18x^{23} }{ 6 } $. Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{9x^{23}}{6} \cdot 2 & \xlongequal{\text{Step 1}} \frac{9x^{23}}{6} \cdot \frac{2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9x^{23} \cdot 2 }{ 6 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 18x^{23} }{ 6 } \end{aligned} $$ |