Answer
$$(\frac{125i^{12}}{27i^3})^{-2/3}=(\frac{125}{-27i})^{-2/3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(\frac{125i^{12}}{27i^3})^{-2/3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(\frac{125}{27i^3})^{-2/3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(\frac{125}{-27i})^{-2/3}\end{aligned} $$ | |
| ① | $$ 125i^{12} = 125 \cdot i^{4 \cdot 3 + 0} =
125 \cdot \left( i^4 \right)^{ 3 } \cdot i^0 =
125 \cdot 1^{ 3 } \cdot 1 =
125 \cdot 1 $$ |
| ② | $$ 27i^3 = 27 \cdot \color{blue}{i^2} \cdot i =
27 \cdot ( \color{blue}{-1}) \cdot i =
-27 \cdot \, i $$ |
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