Question

(- 16) ^ (1/4) complex number??​✨​​

Answer 1

`~\hspace{7em}\textit{rational exponents} \\\\ a^{( n)/( m)} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-( n)/( m)} \implies \cfrac{1}{a^{( n)/( m)}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill`

`(-16)^{(1)/(4)}\implies \sqrt[4]{-16}\implies \sqrt[4]{-2^4}\implies \sqrt[4]{-1\cdot 2^4}\implies \sqrt[4]{-1}\cdot \sqrt[4]{2^4} \\\\\\ (-1)^{(1)/(4)}\cdot 2\implies (-1)^{(1)/(2)\cdot (1)/(2)}\cdot 2\implies ((-1)^{(1)/(2)})^{(1)/(2)}\cdot 2\implies (√(-1))^{(1)/(2)}\cdot 2 \\\\\\ (i)^{(1)/(2)}\cdot 2\implies {\Large \begin{array}{llll} 2√(i) \end{array}}`