(x - 36) : (2 . 3 mũ 2) = 2 mũ 2 . 3
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1)5x+1 + 6.5x+1 = 875
5x+1 ( 1+6 ) = 875
5x+1 . 7 = 875
5x+1 = 875 : 7
5x+1 = 125
5x+1 = 53
x+1 = 3
x = 3 - 1
x = 2
2)3x+1 + 3x+3 = 810
3x . 3 + 32 . 3x+1 = 810
3x . 3 + 9 . 3x . 3 = 810
3x .3 ( 1 + 9 ) = 810
3x+1 . 10 = 810
3x+1 = 810 : 10
3x+1 = 81
3x+1 = 34
x+1 = 4
x = 4-1
x = 3
a) \(17\cdot85+15\cdot17-120\)
\(=17\cdot\left(85+15\right)-120\)
\(=17\cdot100-120\)
\(=1700-120\)
\(=1580\)
b) \(27\cdot77+24\cdot27-27\)
\(=27\cdot\left(77+24-1\right)\)
\(=27\cdot100\)
\(=2700\)
\(a,\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6=\left(\left(\frac{3}{7}\right)^2\right)^{10}.\frac{3}{7}:\left(\frac{9}{49}\right)^6=\left(\frac{9}{49}\right)^{10}.\frac{3}{7}:\left(\frac{9}{49}\right)^6\)
\(=\left(\left(\frac{9}{49}\right)^{10}:\left(\frac{9}{49}\right)^6\right).\frac{3}{7}=\left(\frac{9}{49}\right)^{10-6}.\frac{3}{7}=\left(\frac{9}{49}\right)^4.\frac{3}{7}=\left(\left(\frac{3}{7}\right)^2\right)^4.\frac{3}{7}\)
\(=\left(\frac{3}{2}\right)^8.\frac{3}{7}=\left(\frac{3}{2}\right)^9\)
\(b,3-\left(-\frac{6}{7}\right)^0+\left(\frac{1}{2}\right)^2:2=3-1+\left(\frac{1}{2}\right)^2.\frac{1}{2}=2+\left(\frac{1}{2}\right)^3=2+\frac{1}{6}=2\frac{1}{6}\)
\(3+3^2+3^3+...+3^{2012}\)
\(=\left(3+3^2+3^3+3^4\right)+...+\left(3^{2009}+3^{2010}+3^{2011}+3^{2012}\right)\)
\(=3\left(1+3+3^2+3^3\right)+...+3^{2009}\left(1+3+3^2+3^3\right)\)
\(=40\left(3+...+3^{2009}\right)⋮40\)
\(^{3^2}\).\(^{3^3}\)+\(2^3\).\(2^2\)
(\(^{2^3}\).\(^{3^3}\))+(\(2^2\).\(^{3^2}\)
=275
\(\left(x-36\right):\left(2.3^2\right)=2^2.3\)
\(\Rightarrow\left(x-36\right):18=12\)
\(\Rightarrow\left(x-36\right)=12.18\)
\(\Rightarrow x-36=216\)
\(\Rightarrow x=216+36\)
\(\Rightarrow x=252\)
(x-36):(2.32)=2.23
⇒ (x-36):(2.9)=2.8
⇒ (x-36):18=16
⇒ x-36=18.16=288
⇒ x=288+36=324