9.6 In the expansion of $(1+x)^{n}$, the fourth term is equal to 0.96. Find the values of $x$ and $n$, if the sum of the binomial coefficients is 1024.
9.6 Since the sum of the binomial coefficients is equal to $2^{n}$, and $1024=2^{10}$, then $n=10$. Using formula (9.9), we find the fourth term of the expansion

$$
T_{4}=C_{n}^{3} x^{3}=\frac{10 \cdot 9 \cdot 8}{1 \cdot 2 \cdot 3} x^{3}=120 x^{3}
$$

According to the condition, $120 x^{3}=0.96$, from which $x^{3}=0.008$, i.e. $x=0.2$.

Answer: $x=0.2 ; n=10$.