Question
Answer
$$4{f^4}^2 \cdot \dfrac{f}{8}f^{10}=\dfrac{4f^{19}}{8}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4{f^4}^2\frac{f}{8}f^{10}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4\cdot1f^8\frac{f}{8}f^{10} \xlongequal{ } \\[1 em] & \xlongequal{ }4f^8\frac{f}{8}f^{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4f^9}{8}f^{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{4f^{19}}{8}\end{aligned} $$ | |
| ① | $$ \left( f^4 \right)^2 = 1^2 \left( f^4 \right)^2 = f^8 $$ |
| ② | Multiply $4f^8$ by $ \dfrac{f}{8} $ to get $ \dfrac{ 4f^9 }{ 8 } $. Step 1: Write $ 4f^8 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 4f^8 \cdot \frac{f}{8} & \xlongequal{\text{Step 1}} \frac{4f^8}{\color{red}{1}} \cdot \frac{f}{8} \xlongequal{\text{Step 2}} \frac{ 4f^8 \cdot f }{ 1 \cdot 8 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4f^9 }{ 8 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{4f^9}{8} $ by $ f^{10} $ to get $ \dfrac{ 4f^{19} }{ 8 } $. Step 1: Write $ f^{10} $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{4f^9}{8} \cdot f^{10} & \xlongequal{\text{Step 1}} \frac{4f^9}{8} \cdot \frac{f^{10}}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4f^9 \cdot f^{10} }{ 8 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4f^{19} }{ 8 } \end{aligned} $$ |
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