\(\left(\sqrt{4^2}+\sqrt{\left(-4\right)^2}\right).\sqrt{4^{-3}}-\sqrt{3^{-4}}\)
\(=\left(4+4\right).\sqrt{4^{-3}}-\sqrt{3^{-4}}\)
\(=8.\sqrt{4^{-3}}-\sqrt{3^{-4}}\)
\(=8.\sqrt{\frac{1}{4^3}}-\sqrt{\frac{1}{3^4}}\)
\(=8.\frac{1}{8}-\frac{1}{9}\)
\(=1-\frac{1}{9}=\frac{8}{9}\)