Question
Answer
$$\dfrac{48x^5y^3}{y^4}x^2\dfrac{y}{6x^3y^2}=\dfrac{48x^7y^4}{6x^3y^6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{48x^5y^3}{y^4}x^2\frac{y}{6x^3y^2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{48x^5y^3}{y^4}\frac{x^2y}{6x^3y^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{48x^7y^4}{6x^3y^6}\end{aligned} $$ | |
| ① | Multiply $x^2$ by $ \dfrac{y}{6x^3y^2} $ to get $ \dfrac{ x^2y }{ 6x^3y^2 } $. Step 1: Write $ x^2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} x^2 \cdot \frac{y}{6x^3y^2} & \xlongequal{\text{Step 1}} \frac{x^2}{\color{red}{1}} \cdot \frac{y}{6x^3y^2} \xlongequal{\text{Step 2}} \frac{ x^2 \cdot y }{ 1 \cdot 6x^3y^2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2y }{ 6x^3y^2 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{48x^5y^3}{y^4} $ by $ \dfrac{x^2y}{6x^3y^2} $ to get $ \dfrac{ 48x^7y^4 }{ 6x^3y^6 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{48x^5y^3}{y^4} \cdot \frac{x^2y}{6x^3y^2} & \xlongequal{\text{Step 1}} \frac{ 48x^5y^3 \cdot x^2y }{ y^4 \cdot 6x^3y^2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 48x^7y^4 }{ 6x^3y^6 } \end{aligned} $$ |
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