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a)3,7+(-10)+4,78+6,3
=((3,7+6,3+(-10))+4,78)
=10-10+4,78=4,78
b) -4,1 + (-13,7 ) + 59 + (-59 ) + ( -6,3)
=(-59+59)+(-13,7+-6,3)-4,1
=0-20-4,1=-24,1
6,3 + (-3,7) + 2,4 + (-0,3)
= (6,3 + 2,4) + [(-3,7) + (-0,3)]
= 8,7 + [-(3,7+0,3)]
= 8,7+(-4)
= 4,7
\(\dfrac{16^3.3^{10}+120.6^9}{4^6.3^{12}+6^{11}}=\dfrac{\left(2^4\right)^3.3^{10}+3.5.2^3.\left(2.3\right)^9}{\left(2^2\right)^6.3^{12}+\left(2.3\right)^{11}}\)
\(=\dfrac{2^{12}.3^{10}+3.5.2^3.2^9.3^9}{2^{12}.3^{12}+2^{11}.3^{11}}=\dfrac{2^{12}.3^{10}+5.2^{12}.3^{10}}{2^{12}.3^{12}+2^{11}.3^{11}}\)
\(=\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}.\left(2.3+1\right)}\)\(=\dfrac{2^{12}.3^{10}.6}{2^{11}.3^{11}.7}=\dfrac{2.2}{7}=\dfrac{4}{7}\)
6,3 + ( -3,7 ) + 2,4 + ( -0,3 )
= ( 6,3 + 2,4 ) + [( -3,7 ) + ( -0,3 )]
= 8,7 - 4
= 4,7
6,3+(-3,7)+2,4+(-0,3)
=(6,3+2,4)+[(-3,7)+(-0,3)]
=8,7+(-4)
=8,7-4
=4,7
\(6,3+\left(-3,7\right)+2,4+\left(-0,3\right)\)
\(=\left[6,3+2,4\right]+\left[\left(-3,7\right)+\left(-0,3\right)\right]\)
\(=8,7+-4\)
\(=4,7\)
\(6.3+\left(-3.7\right)+2.4+\left(-0.3\right)\)
\(=\left(6.3-0.3\right)-\left(3.7-2.4\right)\)
\(=6-1.3=-4.7\)
\(2.9+3.7+\left(-4.2\right)+\left(-2.9\right)+4.2\)
\(=\left(2.9-2.9\right)+3.7+\left(4.2-4.2\right)\)
\(=3.7\)
d, (-6,5) . 2,8 + 2,8 . (-3,5)
= 2,8 . [(-6,5) - 3,5]
= 2,8 . -10
= -28
**** **** ****
a)6,3+(-3,7)+2,4+(-0,3)=[6,3+2,4]+[(-3,7)+(-0,3)]=8,7+(-4)=8,7-4=4,7
b)(-4,9)+5,5+4,9+(-5,5)=[(-4,9)+4,9]+[5,5+(-5,5)=(4,9-4,9)+(5,5-5,5)=0+0=0
c)2,9+3,7+(-4,2)+(-2,9)+4,2=3,7+[2,9+(-2,9)]+[4,2+(-4,2)]=3,7+(2,9-2,9)+(4,2-4,2)=3,7+0+0=3,7
d)(-6,5).2,8+2,8.(-3,5)=2,8.[(-6,5)+(-3,5)]=2,8.(-10)=(-28)
\(\frac{10^3+2.5^3+5^3}{55}-\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)\(=\frac{2^3.5^3+2.5^3+5^3}{5.11}-\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{5^3\left(2^3+2+1\right)}{5.11}-\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{5^2.11}{11}-\frac{2.6}{3.5}=25-\frac{4}{5}=\frac{121}{5}\)
\(3,7+\left(-10\right)+4,78+6,3\)
\(=\left(3,7+6,3\right)+\left(-10\right)+4,78\)
\(=10+\left(-10\right)+4,78\)
\(=0+4,78=4,78\)
\(A=3,7+(-10)+4,78+6,3\)
\(A=(3,7+6,3)+(-10)+4,78\)
\(A=10+(-10)+4,78\)
\(A=[10+(-10)]+4,78\)
\(A=0+4,78\)
\(A=4,78\)