6.1 Exponents practice 2

Which of the following numbers is negative?

If [math]2^{-4}\cdot4^{-3}\cdot8^{\frac{4}{9}}=2^a[/math] where [math]a[/math] is a rational number, what is the value of [math]a[/math]?

If [math]\displaystyle{\frac{\sqrt[3]{3\sqrt{3}}}{3^{-\frac{1}{3}}}}=3^a[/math] where [math]a[/math] is a rational number, what is the value of [math]a[/math]?

[math]\displaystyle{\frac{(ab^{-2}c^3)^{-0.5}}{(a^{-3}b^2c^{-1})^{-1.5}}}=[/math]

[math]\displaystyle{\frac{4^x-4^{-x}}{2^x-2^{-x}}}=[/math]

[math]a^{b^0}\times b^{0^a}=[/math]

[math]x^{3y-4}\times \sqrt{x}^{9-6y}=[/math]

Find [math]a^2[/math] such that [math](((2^a)^a)^a)^a=16[/math]. If you have two or more answers, write the smallest one.

If [math]a^{2x}=3[/math], what is the value of [math]\displaystyle{\frac{a^{3x}+a^{-3x}}{a^x-a^{-x}}}[/math]?