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a: \(\Leftrightarrow2^x=1024\cdot3+1024\cdot7776+7776\cdot5\)
\(\Leftrightarrow2^x=8004576\)
hay \(x\in\varnothing\)
b: \(\Leftrightarrow x\left(x+3\right)^{100}-\left(x+3\right)^{100}=0\)
\(\Leftrightarrow\left(x+3\right)^{100}\left(x-1\right)=0\)
=>x=-3 hoặc x=1

\(\dfrac{5.4^6.9^5+6^{10}.10^2}{8^4.3^{12}-6^{11}}=\dfrac{5.\left(2^2\right)^6.\left(3^2\right)^5+\left(2.3\right)^{10}.\left(5.2\right)^2}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}\)
=\(\dfrac{5.2^{12}.3^{10}+2^{10}.3^{10}.5^2.2^2}{2^{12}.3^{12}-2^{11}.3^{11}}=\dfrac{5.2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}\left(2.3-1\right)}\)
=\(\dfrac{5.2.6}{1.3.5}=4\)

ta có
\(2.\left(\dfrac{1}{3}+\dfrac{1}{13}+\dfrac{1}{11}+\dfrac{1}{6}\right)\) \(5.\left(\dfrac{1}{4}+\dfrac{1}{7}+\dfrac{1}{6}+\dfrac{1}{11}\right)\)
_______________________ X ________________________
\(4.\left(\dfrac{1}{3}+\dfrac{1}{13}+\dfrac{1}{11}+\dfrac{1}{6}\right)\) \(9.\left(\dfrac{1}{4}+\dfrac{1}{7}+\dfrac{1}{6}\dfrac{1}{11}\right)\)
= \(\dfrac{2}{4}X\dfrac{5}{9}\)= \(\dfrac{10}{36}\)= \(\dfrac{5}{18}\)

a)56+48=104
b)343-216-125=2
c)1296-32*27=1296-864=432
d)=0(vì các số *với 0 đều =0(\(2^4\)-4\(^2\)=0)
a) \(2^3.7+3^2.6=8.7+9.6\)
\(=56+54\)
\(=110\)
b) \(7^3-6^3-5^3=343-216-125\)
\(=2\)
c) \(6^4-2^5.3^3=1296-32.27\)
\(=1296-864\)
\(=432\)
d) \(\left(7^9-9^7\right)\left(6^8-8^6\right)\left(3^5-5^3\right)\left(2^4-4^2\right)\)
\(=\left(7^9-9^7\right)\left(6^8-8^6\right)\left(3^5-5^3\right).0\)
\(=0\)
NHỚ K CHO MÌNH NHÉ !

\(=81.\dfrac{12.\left(1-\dfrac{1}{7}-\dfrac{1}{289}-\dfrac{1}{85}\right)}{4.\left(1-\dfrac{1}{7}-\dfrac{1}{289}-\dfrac{1}{85}\right)}:\dfrac{5.\left(1+\dfrac{1}{13}+\dfrac{1}{169}+\dfrac{1}{91}\right)}{6.\left(1+\dfrac{1}{13}+\dfrac{1}{169}+\dfrac{1}{91}\right)}.\dfrac{158}{711}\)
\(=81.\dfrac{12}{4}:\dfrac{5}{6}.\dfrac{2}{9}\)
\(=243:\dfrac{5}{6}.\dfrac{2}{9}\)
\(=\dfrac{1458}{5}.\dfrac{2}{9}\)
\(=\dfrac{324}{5}\)

Ta có: \(\left(5^7+7^5\right)\cdot\left(6^8+8^6\right)\left(2^4-4^2\right)\)
\(=\left(5^7+7^5\right)\left(6^8+8^6\right)\left(16-16\right)\)
=0
Ta có: \(\left(\right. 5^{7} + 7^{5} \left.\right) \cdot \left(\right. 6^{8} + 8^{6} \left.\right) \left(\right. 2^{4} - 4^{2} \left.\right)\)
\(= \left(\right. 5^{7} + 7^{5} \left.\right) \left(\right. 6^{8} + 8^{6} \left.\right) \left(\right. 16 - 16 \left.\right)\)
=0

a) \(2^{3x+2}=4^{x+5}\Leftrightarrow2^{3x+2}=2^{2\left(x+5\right)}\Leftrightarrow2^{3x+2}=2^{2x+10}\)
\(\Rightarrow3x+2=2x+10\Leftrightarrow3x+2-2x-10\)
\(\Leftrightarrow x-8=0\Leftrightarrow x=8\) vậy \(x=8\)

47 . 34 . 96 : 613
= 214 . 34 . 312 : 313 : 213
= 2 . 316 : 313
= 2 . 33
= 2 . 27
= 54
\(4^6=4\cdot4\cdot4\cdot4\cdot4\cdot4\)
\(4^6=4096\)
4^6=4.4.4.4.4.4=4096