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