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a: \(=703-140:\left(38+32\right)-17^{15}:17^{13}\)
\(=703-140:70-17^2\)
\(=701-289=412\)
b: \(=1024:32+140:\left(38+32\right)+23^2-7^2\)
\(=32+140:70+529-49\)
\(=32+4+480=516\)
c: \(=17^4\cdot17:17^3-14\cdot4:8\)
\(=17^2-7=289-7=282\)
\(\left(1^2+2^3+3^4+4^5\right)\left(1^3+2^3+3^3+4^3\right)\left(3^8-81^2\right)\\ =\left(1^2+2^3+3^4+4^5\right)\left(1^3+2^3+3^3+4^3\right)\left[3^8-\left(3^4\right)^2\right]\\ =\left(1^2+2^3+3^4+4^5\right)\left(1^3+2^3+3^3+4^3\right)\left(3^8-3^8\right)\\ =\left(1^2+2^3+3^4+4^5\right)\left(1^3+2^3+3^3+4^3\right).0=0\)
\(\left(1^2+2^3+3^4+4^5\right)\left(1^3+2^3+3^3+4^3\right)\left(3^8-81^2\right)=\left(1^2+2^3+3^4+4^5\right)\left(1^3+2^3+3^3+4^3\right)\left(3^8-3^8\right)=\left(1^2+2^3+3^4+4^5\right)\left(1^3+2^3+3^3+4^3\right).0=0\)
47. (23 + 50)- 23. ( 47+50 )
= 47. 23+ 47. 50- 23. 47 - 23. 50
=47. 50 - 23. 50
= 50 .( 47 -23)
=50. 24 = 1200
\(A=\frac{7}{3\times13}+\frac{7}{13\times23}+...+\frac{7}{53\times63}\)
\(A=\frac{7}{10}.\left[\left(\frac{1}{3}-\frac{1}{13}\right)+\left(\frac{1}{13}-\frac{1}{23}\right)+....+\left(\frac{1}{53}-\frac{1}{63}\right)\right]\)
\(A=\frac{7}{10}.\left(\frac{1}{3}-\frac{1}{13}+\frac{1}{13}-\frac{1}{23}+....+\frac{1}{53}-\frac{1}{63}\right)\)
\(A=\frac{7}{10}.\left(\frac{1}{3}-\frac{1}{63}\right)\)
\(A=\frac{7}{10}.\frac{20}{63}\)
\(A=\frac{2}{9}\)
1) (-37) + 14 + 26 + 37
= [(-37) + 37] + 14 + 26
= 0 + 40
= 40
2) (-24) + 6 + 10 + 24
= [(-24) + 24] + 6 + 10
= 0 + 16
= 16
3) 15 + 23 + (-25) + (-23)
= 15 + (-25) + [(-23) + 23]
= -10 + 0
= -10
4) 60 + 33 + (-50) + (-33)
= 60 + (-50) + [(-33) + 33]
= 10 + 0
= 10
A=7*(1/3*13+1/13*23+1/23*33+1/33*43+1/43*53+1/53*63)
A=7/10(1/3-1/13+1/13-1/23+1/23-1/33+1/33-1/43+1/43-1/53+1/53-1/63)
A=7/10*(1/3-1/63)
A=7/10*20/63
A=2/9