Find the exact value of the logarithm without using a calculator. \( \log _{4} \sqrt[5]{4} \) \( \log _{4} \sqrt[5]{4}=\square \) (Type an integer or a simplified fraction.)

Hisoblang: \( \sqrt{66^{2}-44^{2}-22^{2}} \) \( \begin{array}{llll}\text { A) } 22 & \text { B) } 44 & \text { C) } 0 & \text { D) } 33\end{array} \)

e) \( \sqrt[2]{\left(\frac{49}{9}\right)^{11} \cdot\left(\frac{49}{9}\right)^{-4}:\left(\frac{98}{18}\right)^{6}: \frac{196}{36}+[3-(0, \hat{6}-1)]^{2}}= \)

Write the following recurring decimal as a simplified commor fraction. \( \mathbf{0 , 7 4} \)

2. The value of \( \frac{(0.1)^{2}-(0.01)^{2}}{0.0001}+1 \) is

A population of a bacteria colony doubles every 3 hours. If there are currently 500 bacteria, how many will there be after 12 hours?