6.1 Exponents (in class)

Evaluate [math]\left(81^{-\frac{1}{2}}\cdot64^{\frac{1}{3}}\right)^{\frac{1}{2}}[/math]

If [math]\left(\displaystyle{\frac{-2a^{-2}b}{6ab^{-3}c^0}}\right)^{-2}=xa^yb^z[/math] where [math]x, y[/math], and [math]z[/math] are integers, what is the value of [math]x+y+z[/math]?

If [math]2^3\cdot\sqrt[3]{4}\cdot\sqrt{8\cdot\sqrt[4]{16}}=2^a[/math] where [math]a[/math] is a constant, what is the value of [math]a[/math]?

Let [math]a^x+a^{-x}=5[/math]. Evaluate

(a) [math]a^{2x}+a^{-2x}[/math]

(b) [math]a^{3x}+a^{-3x}[/math]

Let [math]2^x=3^y=216[/math]. Evaluate [math]\displaystyle{\frac{1}{x}+\frac{1}{y}}[/math].