Question
Answer
$${x^2}^3 \cdot \dfrac{5x}{6x^2\cdot15x^3}=\dfrac{5x^7}{90x^5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}{x^2}^3\frac{5x}{6x^2\cdot15x^3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^6\frac{5x}{6x^2\cdot15x^3} \xlongequal{ } \\[1 em] & \xlongequal{ }x^6\frac{5x}{90x^5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5x^7}{90x^5}\end{aligned} $$ | |
| ① | $$ \left( x^2 \right)^3 = 1^3 \left( x^2 \right)^3 = x^6 $$ |
| ② | Multiply $x^6$ by $ \dfrac{5x}{90x^5} $ to get $ \dfrac{ 5x^7 }{ 90x^5 } $. Step 1: Write $ x^6 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} x^6 \cdot \frac{5x}{90x^5} & \xlongequal{\text{Step 1}} \frac{x^6}{\color{red}{1}} \cdot \frac{5x}{90x^5} \xlongequal{\text{Step 2}} \frac{ x^6 \cdot 5x }{ 1 \cdot 90x^5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^7 }{ 90x^5 } \end{aligned} $$ |
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