Question

The expression 8^-2/3 is equivalent to?

Answer 1

`Use:\\a^(-n)=\left((1)/(a)\right)^n\\\\a^(m)/(n)=(\sqrt[n]{a})^m\\\\8^{-(2)/(3)}=\left((1)/(8)\right)^(2)/(3)=\left(\sqrt[3]{(1)/(8)}\right)^2=\left((1)/(2)\right)^2=\boxed{(1)/(4)}`



`or\ use:\\\\\left(a^n\right)^m=a^(n\cdot m)\\\\a^(-n)=\left((1)/(a)\right)^n\\\\8^{-(2)/(3)}=\left(2^3\right)^{-(2)/(3)}=2^{3*(-(2)/(3))}=2^(-2)=\left((1)/(2)\right)^2=(1)/(2)*(1)/(2)=\boxed{(1)/(4)}`