Exercise 1. Calculate the number

$$
\frac{4^{8}}{8^{4}}
$$

Only a numerical answer is expected here.
Solution to Exercise 1 The idea is to notice that 4 and 8 are both powers of 2, which will allow us to avoid explicitly calculating the numerator and the denominator. Indeed, by using the formula $\left(a^{b}\right)^{c}=a^{b c}$, we get

$$
\frac{4^{8}}{8^{4}}=\frac{\left(2^{2}\right)^{8}}{\left(2^{3}\right)^{4}}=\frac{2^{2 \times 8}}{2^{3 \times 4}}=\frac{2^{16}}{2^{12}}=2^{16-12}=2^{4}=16
$$

Graders' comments: Apart from the majority of students who calculate correctly, there is a large number of calculation errors. It is good to review your calculations to avoid such pitfalls.