Answer
$$(3i^9)^3xi^{12}=27i^3x\cdot1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3i^9)^3xi^{12}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(3i)^3x\cdot1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}27i^3x\cdot1\end{aligned} $$ | |
| ① | $$ 3i^9 = 3 \cdot i^{4 \cdot 2 + 1} =
3 \cdot \left( i^4 \right)^{ 2 } \cdot i^1 =
3 \cdot 1^{ 2 } \cdot i =
3 \cdot i $$$$ i^{12} = i^{4 \cdot 3 + 0} =
\left( i^4 \right)^{ 3 } \cdot i^0 =
1^{ 3 } \cdot 1 =
1 $$ |
| ② | $$ \left( 3i \right)^3 = 3^3i^3 = 27i^3 $$ |
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