The answer is 8 and heres why:
[tex] 64^{\frac{3}{6}}
\\\frac{3}{6}=\frac{1}{2}
\\
\\64^{\frac{1}{2}}
\\
\\\mathrm{Factor\:the\:number:\:}\:64=8^2
\\\left(8^2\right)^{\frac{1}{2}}
\\
\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}
\\\left(8^2\right)^{\frac{1}{2}}=8^{2\cdot \frac{1}{2}}=8
[/tex]
And that is how you solve this promblem :-)