Question
Answer
$$3\cdot\dfrac{t^2}{(2t^5)^2}=\dfrac{3t^2}{4t^{10}}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3 \cdot \frac{t^2}{(2t^5)^2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3 \cdot \frac{t^2}{4t^{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3t^2}{4t^{10}}\end{aligned} $$ | |
| ① | $$ \left( 2t^5 \right)^2 = 2^2 \left( t^5 \right)^2 = 4t^{10} $$ |
| ② | Multiply $3$ by $ \dfrac{t^2}{4t^{10}} $ to get $ \dfrac{ 3t^2 }{ 4t^{10} } $. Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 3 \cdot \frac{t^2}{4t^{10}} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{t^2}{4t^{10}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot t^2 }{ 1 \cdot 4t^{10} } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3t^2 }{ 4t^{10} } \end{aligned} $$ |
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