13. What is the value of $\sqrt[4]{2^{20}+2^{27}+2^{31}+2^{32}+2^{37}+2^{40}}$?
13. The answer is 1056. Once a factor of $2^{20}$ is collected under the fourth root, one is reduced to calculating $\sqrt[4]{1+2^{7}+2^{11}+2^{12}+2^{17}+2^{20}}$. At this point, it is possible to recognize in the expression under the root the square of the trinomial $1+2^{6}+2^{10}=\left(2^{5}+1\right)^{2}$ or directly verify that it is the fourth power of $2^{5}+1$. The expression as a whole thus has the value $2^{5}\left(2^{5}+1\right)$, which is 1056.