$$27c^4d^{715}c^3 \cdot \dfrac{d^5}{3}c^2d^3=\dfrac{27c^9d^{723}}{3}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}27c^4d^{715}c^3\frac{d^5}{3}c^2d^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}27c^7d^{715}\frac{d^5}{3}c^2d^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{27c^7d^{720}}{3}c^2d^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{27c^9d^{720}}{3}d^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{27c^9d^{723}}{3}\end{aligned} $$ | |
| ① | $$ 27 c^4 d^{715} c^3 = 27 c^{4 + 3} d^{715} = 27 c^7 d^{715} $$ |
| ② | Multiply $27c^7d^{715}$ by $ \dfrac{d^5}{3} $ to get $ \dfrac{ 27c^7d^{720} }{ 3 } $. Step 1: Write $ 27c^7d^{715} $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 27c^7d^{715} \cdot \frac{d^5}{3} & \xlongequal{\text{Step 1}} \frac{27c^7d^{715}}{\color{red}{1}} \cdot \frac{d^5}{3} \xlongequal{\text{Step 2}} \frac{ 27c^7d^{715} \cdot d^5 }{ 1 \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 27c^7d^{720} }{ 3 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{27c^7d^{720}}{3} $ by $ c^2 $ to get $ \dfrac{ 27c^9d^{720} }{ 3 } $. Step 1: Write $ c^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{27c^7d^{720}}{3} \cdot c^2 & \xlongequal{\text{Step 1}} \frac{27c^7d^{720}}{3} \cdot \frac{c^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 27c^7d^{720} \cdot c^2 }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 27c^9d^{720} }{ 3 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{27c^9d^{720}}{3} $ by $ d^3 $ to get $ \dfrac{ 27c^9d^{723} }{ 3 } $. Step 1: Write $ d^3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{27c^9d^{720}}{3} \cdot d^3 & \xlongequal{\text{Step 1}} \frac{27c^9d^{720}}{3} \cdot \frac{d^3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 27c^9d^{720} \cdot d^3 }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 27c^9d^{723} }{ 3 } \end{aligned} $$ |