1. Solve the equation for $x$: $3^{2x-1} = \frac{\sqrt{3}}{9}$. $x = $ ___
2. Solve the equation for $x$: $27^{x+2} = 81^{x-1}$. $x = $ ___
3. Solve the equation for $x$: $16^{2-3x} = 64^{x+5}$. $x = $ ___
4. Which of the following pairs of functions have identical graphs? Consider $h(x) = 6^x$, $k(x) = (\frac{1}{6})^x$, $m(x) = 6^{-x}$, and $n(x) = \frac{1}{6^x}$.
5. Solve for the larger value of $x$: $5^{x^2-x-4} = 25$. $x = $ ___
6. Solve the equation for $x$: $5^{x+2} = 25^{4/3}$. $x = $ ___
7. An outbreak of a disease doubles the number of cases every 6 days. If there are 26 cases initially, after how many days will there be 106,496 cases? ___
8. Use the laws of exponents to simplify the expression $b^{t/2} b^{t/2}$.
9. Use the laws of exponents to simplify the expression $(3^x)^4$.
10. Use the laws of exponents to simplify the expression $\frac{8^{2x}}{8^x}$.