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3C=3^4+3^5+...+3^2019
=>2C=3^2019-3
=>\(C=\dfrac{3^{2019}-3}{2}\)
a: \(2^{10}:2^8=2^2=4\)
b: \(4^6:4^3=4^3=64\)
c: \(8^5:8^4=8^{5-4}=8\)
c: \(7^4:7^4=7^0=1\)
a: \(=2^6\cdot2^{20}=2^{26}\)
b: \(=3^9\cdot3^8\cdot3^2\cdot2\cdot13=3^{19}\cdot2\cdot13\)
a) \(\left(6x-5y\right)^2=36x^2-60xy+25y^2\)
b) \(\left(4x-1\right)^2=16x^2-8x+1\)
c) \(\left(x+2\right)^2=x^2+4x+4\)
d) \(x^2-64=\left(x-8\right)\left(x+8\right)\)
e) \(4x^2-64=\left(2x-8\right)\left(2x+8\right)\)
f) \(25x^2-4=\left(5x-2\right)\left(5x+2\right)\)
g) \(\left(x+1\right)^3=x^3+3x^2+3x+1\)
h) \(\left(x-3\right)^3=x^3-9x^2+27x-27\)
k) \(x^3+8=\left(x+2\right)\left(x^2-2x+4\right)\)
l) \(x^3-125=\left(x-5\right)\left(x^2+5x+25\right)\)
y) \(27y^3-1=\left(3y-1\right)\left(9y^2+3y+1\right)\)
a: \(7\cdot3^x=5\cdot3^7+2\cdot3^7\)
\(\Leftrightarrow7\cdot3^x=7\cdot3^7\)
=>3x=37
hay x=7
b: \(4^{x+3}-3\cdot4^{x+1}=13\cdot4^{11}\)
\(\Leftrightarrow4^{x+1}\left(4^2-3\right)=13\cdot4^{11}\)
=>x+1=11
hay x=10
d: \(\left(x-1\right)^{13}=\left(x-1\right)^{12}\)
\(\Leftrightarrow\left(x-1\right)^{12}\left(x-2\right)=0\)
hay \(x\in\left\{1;2\right\}\)
\(4S=4+4^2+4^3+...+4^{2019}\)
=>3S=4^2019-1
hay \(S=\dfrac{4^{2019}-1}{3}\)