Problem: 810+41084+411=\sqrt{\dfrac{8^{10}+4^{10}}{8^{4}+4^{11}}}=84+411810+410​​=
Answer Choices:
A. 2\sqrt{2}2​
B. 161616
C. 323232
D. 122/312^{2 / 3}122/3
E. 512.5512.5512.5
Solution:
810+41084+411=(23)10+(22)10(23)4+(22)11=230+220212+222=220(210+1)212(1+210)\sqrt{\dfrac{8^{10}+4^{10}}{8^{4}+4^{11}}}=\sqrt{\dfrac{\left(2^{3}\right)^{10}+\left(2^{2}\right)^{10}}{\left(2^{3}\right)^{4}+\left(2^{2}\right)^{11}}}=\sqrt{\dfrac{2^{30}+2^{20}}{2^{12}+2^{22}}}=\sqrt{\dfrac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(1+2^{10}\right)}} 84+411810+410​​=(23)4+(22)11(23)10+(22)10​​=212+222230+220​​=212(1+210)220(210+1)​​
=28=24=16.=\sqrt{2^{8}}=2^{4}=16 . =28​=24=16.