Question

How to solve 8 to the power of negative one third

Answer 1

`8^{-(1)/(3)}=(1)/(8^(1)/(3))=(1)/(\sqrt[3]8)=(1)/(2)\\\\Used:\\\\a^(-n)=(1)/(a^n)\\\\a^(1)/(n)=\sqrt[n]{a}\\------------------------\\Other\ method\\\\8=2^3\\\\8^{-(1)/(3)}=(2^3)^{-(1)/(3)}=2^{3\cdot\left(-(1)/(3)\right)}=2^(-1)=(1)/(2)\\\\Used:\\\\(a^n)^m=a^(n\cdot m)\\\\a^(-n)=(1)/(a^n)`