Algebra
# Negative and Rational Exponents

Evaluate $\large \left(\frac{1}{256} \right)^{-\frac{5}{8 }}.$

If $a>0$, simplify

$\left( a^{\frac{2}{3}} + a^{-\frac{1}{3}} \right)^3 + \left( a^{\frac{2}{3}} - a^{-\frac{1}{3}} \right)^3.$

Evaluate

$\left( \sqrt{2 + \sqrt{3}} - \sqrt{2 - \sqrt{3}} \right)^{\frac13}.$

If $x = \dfrac{3^{\frac{1}{5}} + 3^{ -\frac{1}{5}} }{2}$, evaluate

$\left( x + \sqrt{x^2 - 1} \right)^{10}.$