- Simplify the following expressions:
- $(\frac{7}{9})^0$
- $y^{-2}y^{-5}$
- $(-xy^2)^{-4}$
- $(y^3y^4)^4$
- $y^2y^5$
- Bacteria grow by doubling every 10 minutes. Suppose you are infected by one bacteria, and allow it to grow for 4 hours. Then you begin frantically washing and rewashing your hands with a soap that is only one-third ($\frac{1}{3}$) effective (so it kills one-third of the bacteria present each time you use it). How many times will you have to wash your hands to get the number of bacteria down below 1? Show your work using exponents to represent the growth and the washing phases.