Simplify: $\left[5\left(8^{\frac{1}{3}}+27^{\frac{1}{3}}\right)^{3}\right]^{\frac{1}{4}}$

Simplify $7^{\frac{1}{4}} \cdot 12^{\frac{1}{4}}$.

Fill in the blank to make the following statement true:
$(64)^{-\frac{1}{6}} = \ldots \ldots$

Simplify:
$(i)$ $2^{\frac{2}{3}} \cdot 2^{\frac{1}{3}}$
$(ii)$ $\left(3^{\frac{1}{5}}\right)^{4}$
$(iii)$ $\frac{7^{\frac{1}{5}}}{7^{\frac{1}{3}}}$
$(iv)$ $13^{\frac{1}{5}} \cdot 17^{\frac{1}{5}}$

State whether the following statement is true or false:
$(-1)^{11} = -1$

State whether the following statement is true or false:
$(-5)^{2} = -25$