Answer
$$-6\cdot\frac{x^3}{2^5}x=\frac{6x^4}{32}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-6 \cdot \frac{x^3}{2^5}x& \xlongequal{ }6 \cdot \frac{x^3}{32}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6x^3}{32}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6x^4}{32}\end{aligned} $$ | |
| ① | Multiply $6$ by $ \dfrac{x^3}{32} $ to get $ \dfrac{ 6x^3 }{ 32 } $. Step 1: Write $ 6 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 6 \cdot \frac{x^3}{32} & \xlongequal{\text{Step 1}} \frac{6}{\color{red}{1}} \cdot \frac{x^3}{32} \xlongequal{\text{Step 2}} \frac{ 6 \cdot x^3 }{ 1 \cdot 32 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6x^3 }{ 32 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{6x^3}{32} $ by $ x $ to get $ \dfrac{ 6x^4 }{ 32 } $. 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. $$ \begin{aligned} \frac{6x^3}{32} \cdot x & \xlongequal{\text{Step 1}} \frac{6x^3}{32} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 6x^3 \cdot x }{ 32 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6x^4 }{ 32 } \end{aligned} $$ |
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