Question

Answer 1

=\(\dfrac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}\)

=\(\dfrac{2^{30}+2^{20}}{2^{12}+2^{22}}\)

=\(\dfrac{2^{20}.\left(1+2^{10}\right)}{2^{12}.\left(1+2^{10}\right)}\)

=\(\dfrac{2^{20}}{2^{12}}\)

=2⁸=256

Answer 2

\(\dfrac{8^{10}+4^{10}}{8^4+4^{11}}=\dfrac{2^{10}\cdot2^{10}\cdot2^{10}+2^{10}\cdot2^{10}}{2^4\cdot2^4\cdot2^4+2^{11}\cdot2^{11}}=\dfrac{2^{10}\cdot2^{10}\left(2^{10}+1\right)}{2^4\cdot2^4\left(2^4+2^7\cdot2^7\right)}=\dfrac{2^6\cdot2^6\left(2^{10}+1\right)}{2^4+2^7\cdot2^7}=\dfrac{2^6\cdot2^6\left(2^{10}+1\right)}{2^4\left(1+2^{10}\right)}=\dfrac{2^6\cdot2^6}{2^4}=2^2\cdot2^6=4\cdot64=256\)

Answer 3

256