Question
Answer
$$7\cdot\dfrac{{x^4}^3}{(3x^2)^2}=\dfrac{7x^{12}}{9x^4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}7 \cdot \frac{{x^4}^3}{(3x^2)^2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}7 \cdot \frac{x^{12}}{9x^4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{7x^{12}}{9x^4}\end{aligned} $$ | |
| ① | $$ \left( x^4 \right)^3 = 1^3 \left( x^4 \right)^3 = x^{12} $$ |
| ② | $$ \left( 3x^2 \right)^2 = 3^2 \left( x^2 \right)^2 = 9x^4 $$ |
| ③ | Multiply $7$ by $ \dfrac{x^{12}}{9x^4} $ to get $ \dfrac{ 7x^{12} }{ 9x^4 } $. Step 1: Write $ 7 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 7 \cdot \frac{x^{12}}{9x^4} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} \cdot \frac{x^{12}}{9x^4} \xlongequal{\text{Step 2}} \frac{ 7 \cdot x^{12} }{ 1 \cdot 9x^4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x^{12} }{ 9x^4 } \end{aligned} $$ |
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