Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-5x^2y^3\frac{z^4}{15}x^4y^2z\cdot64& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5x^2y^3z^4}{15}x^4y^2z\cdot64 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5x^6y^3z^4}{15}y^2z\cdot64 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{5x^6y^5z^4}{15}z\cdot64 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{5x^6y^5z^5}{15}\cdot64 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{320x^6y^5z^5}{15}\end{aligned} $$ | |
| ① | Multiply $5x^2y^3$ by $ \dfrac{z^4}{15} $ to get $ \dfrac{ 5x^2y^3z^4 }{ 15 } $. Step 1: Write $ 5x^2y^3 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 5x^2y^3 \cdot \frac{z^4}{15} & \xlongequal{\text{Step 1}} \frac{5x^2y^3}{\color{red}{1}} \cdot \frac{z^4}{15} \xlongequal{\text{Step 2}} \frac{ 5x^2y^3 \cdot z^4 }{ 1 \cdot 15 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2y^3z^4 }{ 15 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{5x^2y^3z^4}{15} $ by $ x^4 $ to get $ \dfrac{ 5x^6y^3z^4 }{ 15 } $. Step 1: Write $ x^4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x^2y^3z^4}{15} \cdot x^4 & \xlongequal{\text{Step 1}} \frac{5x^2y^3z^4}{15} \cdot \frac{x^4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^2y^3z^4 \cdot x^4 }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^6y^3z^4 }{ 15 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{5x^6y^3z^4}{15} $ by $ y^2 $ to get $ \dfrac{ 5x^6y^5z^4 }{ 15 } $. 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. $$ \begin{aligned} \frac{5x^6y^3z^4}{15} \cdot y^2 & \xlongequal{\text{Step 1}} \frac{5x^6y^3z^4}{15} \cdot \frac{y^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^6y^3z^4 \cdot y^2 }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^6y^5z^4 }{ 15 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{5x^6y^5z^4}{15} $ by $ z $ to get $ \dfrac{ 5x^6y^5z^5 }{ 15 } $. Step 1: Write $ z $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x^6y^5z^4}{15} \cdot z & \xlongequal{\text{Step 1}} \frac{5x^6y^5z^4}{15} \cdot \frac{z}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^6y^5z^4 \cdot z }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^6y^5z^5 }{ 15 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{5x^6y^5z^5}{15} $ by $ 64 $ to get $ \dfrac{ 320x^6y^5z^5 }{ 15 } $. Step 1: Write $ 64 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5x^6y^5z^5}{15} \cdot 64 & \xlongequal{\text{Step 1}} \frac{5x^6y^5z^5}{15} \cdot \frac{64}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^6y^5z^5 \cdot 64 }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 320x^6y^5z^5 }{ 15 } \end{aligned} $$ |