6. What is the value of $\frac{4^{800}}{8^{400}}$ ?
A $\frac{1}{2^{400}}$
B $\frac{1}{2^{2000}}$
C 1
D $2^{200}$
E $2^{400}$
Solution
E

We have
$$
\begin{aligned}
\frac{4^{800}}{8^{400}} & =\frac{\left(2^{2}\right)^{800}}{\left(2^{3}\right)^{400}} \\
& =\frac{2^{1600}}{2^{1200}} \\
& =2^{1600-1200} \\
& =2^{400}
\end{aligned}
$$

For investigation
6.1 For which integer $n$ is $\frac{27^{900}}{9^{2700}}=3^{n}$ ?