$$\dfrac{2}{3}a^4b^4\dfrac{\dfrac{-3a^2b}{1}}{4}a^5b^7=-\dfrac{6a^{11}b^{12}}{12}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{3}a^4b^4\frac{\frac{-3a^2b}{1}}{4}a^5b^7& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2a^4}{3}b^4(-\frac{3a^2b}{4})a^5b^7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{2a^4b^4}{3}(-\frac{3a^2b}{4})a^5b^7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}(-\frac{6a^6b^5}{12})a^5b^7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}(-\frac{6a^{11}b^5}{12})b^7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}-\frac{6a^{11}b^{12}}{12}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{2}{3} $ by $ a^4 $ to get $ \dfrac{ 2a^4 }{ 3 } $. Step 1: Write $ a^4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{2}{3} \cdot a^4 & \xlongequal{\text{Step 1}} \frac{2}{3} \cdot \frac{a^4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2 \cdot a^4 }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2a^4 }{ 3 } \end{aligned} $$ |
| ② | Divide $ \dfrac{-3a^2b}{1} $ by $ 4 $ to get $ \dfrac{ -3a^2b }{ 4 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{ \frac{-3a^2b}{1} }{4} & \xlongequal{\text{Step 1}} \frac{-3a^2b}{1} \cdot \frac{\color{blue}{1}}{\color{blue}{4}} \xlongequal{\text{Step 2}} \frac{ \left( -3a^2b \right) \cdot 1 }{ 1 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -3a^2b }{ 4 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{2a^4}{3} $ by $ b^4 $ to get $ \dfrac{ 2a^4b^4 }{ 3 } $. Step 1: Write $ b^4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{2a^4}{3} \cdot b^4 & \xlongequal{\text{Step 1}} \frac{2a^4}{3} \cdot \frac{b^4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2a^4 \cdot b^4 }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2a^4b^4 }{ 3 } \end{aligned} $$ |
| ④ | Divide $ \dfrac{-3a^2b}{1} $ by $ 4 $ to get $ \dfrac{ -3a^2b }{ 4 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{ \frac{-3a^2b}{1} }{4} & \xlongequal{\text{Step 1}} \frac{-3a^2b}{1} \cdot \frac{\color{blue}{1}}{\color{blue}{4}} \xlongequal{\text{Step 2}} \frac{ \left( -3a^2b \right) \cdot 1 }{ 1 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -3a^2b }{ 4 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{2a^4b^4}{3} $ by $ \dfrac{-3a^2b}{4} $ to get $ \dfrac{ -6a^6b^5 }{ 12 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{2a^4b^4}{3} \cdot \frac{-3a^2b}{4} & \xlongequal{\text{Step 1}} \frac{ 2a^4b^4 \cdot \left( -3a^2b \right) }{ 3 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ -6a^6b^5 }{ 12 } \end{aligned} $$ |
| ⑥ | Multiply $ \dfrac{-6a^6b^5}{12} $ by $ a^5 $ to get $ \dfrac{ -6a^{11}b^5 }{ 12 } $. Step 1: Write $ a^5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{-6a^6b^5}{12} \cdot a^5 & \xlongequal{\text{Step 1}} \frac{-6a^6b^5}{12} \cdot \frac{a^5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -6a^6b^5 \right) \cdot a^5 }{ 12 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -6a^{11}b^5 }{ 12 } \end{aligned} $$ |
| ⑦ | Multiply $ \dfrac{-6a^{11}b^5}{12} $ by $ b^7 $ to get $ \dfrac{ -6a^{11}b^{12} }{ 12 } $. Step 1: Write $ b^7 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{-6a^{11}b^5}{12} \cdot b^7 & \xlongequal{\text{Step 1}} \frac{-6a^{11}b^5}{12} \cdot \frac{b^7}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -6a^{11}b^5 \right) \cdot b^7 }{ 12 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -6a^{11}b^{12} }{ 12 } \end{aligned} $$ |