Question

M = 8²⁰ + 4 ²⁰ / 4²⁵ + 64 ⁵

Answer 1

\(M=\dfrac{8^{20}+4^{20}}{4^{25}+64^5}\)

\(\Leftrightarrow M=\dfrac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}\)

\(\Leftrightarrow M=\dfrac{2^{60}+2^{40}}{2^{50}+2^{30}}\)

\(\Leftrightarrow M=\dfrac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}\)

\(\Leftrightarrow M=\dfrac{2^{40}}{2^{30}}\)

\(\Leftrightarrow M=2^{10}.\)