Question
Answer
$$\dfrac{48i^{24}+72i^{16}-12i^8}{12i^{12}}=9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{48i^{24}+72i^{16}-12i^8}{12i^{12}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{48+72-12}{12i^{12}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{48+72-12}{12} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{108}{12} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 108 : \color{orangered}{ 12 } }{ 12 : \color{orangered}{ 12 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{9}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}9\end{aligned} $$ | |
| ① | $$ 48i^{24} = 48 \cdot i^{4 \cdot 6 + 0} =
48 \cdot \left( i^4 \right)^{ 6 } \cdot i^0 =
48 \cdot 1^{ 6 } \cdot 1 =
48 \cdot 1 $$$$ 72i^{16} = 72 \cdot i^{4 \cdot 4 + 0} =
72 \cdot \left( i^4 \right)^{ 4 } \cdot i^0 =
72 \cdot 1^{ 4 } \cdot 1 =
72 \cdot 1 $$$$ -12i^8 = -12 \cdot i^{4 \cdot 2 + 0} =
-12 \cdot \left( i^4 \right)^{ 2 } \cdot i^0 =
-12 \cdot 1^{ 2 } \cdot 1 =
-12 \cdot 1 $$ |
| ② | $$ 12i^{12} = 12 \cdot i^{4 \cdot 3 + 0} =
12 \cdot \left( i^4 \right)^{ 3 } \cdot i^0 =
12 \cdot 1^{ 3 } \cdot 1 =
12 \cdot 1 $$ |
| ③ | Simplify numerator $$ \color{blue}{48} + \color{red}{72} \color{red}{-12} = \color{red}{108} $$ |
| ④ | Divide both the top and bottom numbers by $ \color{orangered}{ 12 } $. |
| ⑤ | Remove 1 from denominator. |
This page was created using
Complex Expression calculator