9.7 For what value of $x$ is the fourth term of the expansion $\left(\sqrt{2^{x-1}}+\sqrt[3]{2^{-x}}\right)^{m}$ 20 times greater than $m$, if the binomial coefficient of the fourth term is to the binomial coefficient of the second term as $5: 1 ?$
9.7 The binomial coefficients of the fourth and second terms are $C_{m}^{3}$ and $m$, respectively. Therefore, $\frac{m(m-1)(m-2)}{3!m}=5$, or $(m-1)(m-2)=30$, from which $m=7$. Then the fourth term of the expansion has the form $T_{4}=C_{7}^{3} 2^{2(x-1)} \cdot 2^{-x}$, and we arrive at the equation $C_{7}^{3} 2^{x-2}=140$, from which we find $\frac{7 \cdot 6 \cdot 5}{6} \cdot 2^{x-2}=140$; $2^{x-2}=4 ; x=4$.

Answer: $x=4$.