need a clarification

[spacewater]

\(\displaystyle (-\frac{1}{64})^\frac{-1}{3}\)

When there is a negative exponent for a fraction you flip it the other way around to make it
\(\displaystyle (-\frac{64}{1})^\frac{1}{3}\)

I need a clarification whether this is the proper way to do it or not

 

[Loren]

\(\displaystyle (\frac{2}{5})^{-3}=\frac{1}{(\frac{2}{5})^3}=\frac{1\cdot (\frac{5}{2})^3}{(\frac{2}{5})^3\cdot(\frac{5}{2})^3}=\frac{(\frac{5}{2})^3}{1}=(\frac{5}{2})^3\)

 

[Denis]

Use what Loren showed you as a rule: (x/y)^(-p) = (y/x)^p

 

[spacewater]

\(\displaystyle (-\frac{1}{64})^\frac{-1}{3}\)

When there is a negative exponent for a fraction you flip it the other way around to make it
\(\displaystyle (-\frac{64}{1})^\frac{1}{3}\)

I need a clarification whether this is the proper way to do it or not

\(\displaystyle ^3\sqrt{-64} = - 4\)