Question
Answer
$$(5i)^6=-15625$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5i)^6& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}15625i^6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-15625\end{aligned} $$ | |
| ① | $$ \left( 5i \right)^6 = 5^6i^6 = 15625i^6 $$ |
| ② | $$ 15625i^6 = 15625 \cdot i^{4 \cdot 1 + 2} =
15625 \cdot \left( i^4 \right)^{ 1 } \cdot i^2 =
15625 \cdot 1^{ 1 } \cdot (-1) =
15625 \cdot -1 = -15625 $$ |
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