Question
Answer
$$(5i)^{10}=-9765625$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5i)^{10}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9765625i^{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-9765625\end{aligned} $$ | |
| ① | $$ \left( 5i \right)^{10} = 5^{10}i^{10} = 9765625i^{10} $$ |
| ② | $$ 9765625i^{10} = 9765625 \cdot i^{4 \cdot 2 + 2} =
9765625 \cdot \left( i^4 \right)^{ 2 } \cdot i^2 =
9765625 \cdot 1^{ 2 } \cdot (-1) =
9765625 \cdot -1 = -9765625 $$ |
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