Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
a,\\
{2^7}{.5^7} = {\left( {2.5} \right)^7} = {10^7}\\
b,\\
\left( {{4^{16}}{{.4}^2}} \right):\left( {{4^{20}}:16} \right) = {4^{16 + 2}}:\left( {{4^{20}}:{4^2}} \right) = {4^{18}}:{4^{20 - 2}} = {4^{18}}:{4^{18}} = 1\\
2,\\
a,\\
{x^3} = {8^2}\\
\Leftrightarrow {x^3} = {\left( {{2^3}} \right)^2}\\
\Leftrightarrow {x^3} = {\left( {{2^2}} \right)^3}\\
\Leftrightarrow {x^3} = {4^3}\\
\Leftrightarrow x = 4\\
b,\\
{4^2}.x - {3.2^4} = {2^4}{.2^2}\\
\Leftrightarrow {\left( {{2^2}} \right)^2}.x - {3.2^4} = {2^4}{.2^2}\\
\Leftrightarrow {2^4}.x - {3.2^4} = {2^4}{.2^2}\\
\Leftrightarrow {2^4}.\left( {x - 3} \right) = {2^4}{.2^2}\\
\Leftrightarrow x - 3 = {2^2}\\
\Leftrightarrow x - 3 = 4\\
\Leftrightarrow x = 7\\
c,\\
\left( {{2^3} + 2} \right).x + {3^2}.x.5 + 20 = {3.5^2}\\
\Leftrightarrow \left( {8 + 2} \right).x + 9.x.5 + 20 = 3.25\\
\Leftrightarrow 10x + 45x + 20 = 75\\
\Leftrightarrow 55x = 55\\
\Leftrightarrow x = 1\\
d,\\
27 \le {3^x} \le 243\\
\Leftrightarrow {3^3} \le {3^x} \le {3^5}\\
\Leftrightarrow 3 \le x \le 5\\
\Rightarrow x \in \left\{ {3;4;5} \right\}\\
3,\\
A = 1 + 2 + {2^2} + {2^3} + {2^4} + ..... + {2^{2019}}\\
\Leftrightarrow 2A = 2.\left( {1 + 2 + {2^2} + {2^3} + {2^4} + ..... + {2^{2019}}} \right)\\
\Leftrightarrow 2A = 2 + {2^2} + {2^3} + {2^4} + ..... + {2^{2019}} + {2^{2020}}\\
\Rightarrow 2A - A = \left( {2 + {2^2} + {2^3} + {2^4} + ..... + {2^{2019}} + {2^{2020}}} \right) - \left( {1 + 2 + {2^2} + {2^3} + {2^4} + ..... + {2^{2019}}} \right)\\
\Leftrightarrow A = {2^{2020}} - 1\\
\Rightarrow A = B
\end{array}\)
