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A. 2/3 - (- 1/4)+3/5-(+7/45)-(-5/9)+1/12+1/39
B. 6.(-2/3)^2 - 3(-2/3)^2 - 2 : (-3/2)+4
\(\frac{4^{10}.9^6+3^{12}.8^5}{6^{13}.4-2^{16}.3^{12}}\)
\(=\frac{\left(2^2\right)^{10}.\left(3^2\right)^6+3^{12}.\left(2^3\right)^5}{\left(2.3\right)^{13}.2^2-2^{16}.3^{12}}\)
\(=\frac{2^{20}.3^{12}+3^{12}.2^{15}}{2^{13}.3^{13}.2^2-2^{16}.3^{12}}\)
\(=\frac{2^{20}.3^{12}+3^{12}.2^{15}}{2^{15}.3^{12}.3-3^{12}.2^{16}}\)
\(=\frac{2^4}{3}\)
\(\dfrac{4^{10}.9^6+3^{12}.8^5}{6^{13}.4-2^{16}.3^{12}}\)
\(=\dfrac{\left(2^2\right)^{10}.\left(3^2\right)^6+3^{12}.\left(2^3\right)^5}{\left(2.3\right)^{13}.2^2-2^{16}.3^{12}}\)
\(=\dfrac{2^{20}.3^{12}+3^{12}.2^{15}}{2^{13}.3^{13}.2^2-2^{16}.3^{12}}\)
\(=\dfrac{2^{20}.3^{12}+3^{12}.2^{15}}{2^{15}.3^{13}-2^{16}.3^{12}}\)
\(=\dfrac{2^{15}.3^{12}.\left(2^5+1\right)}{2^{15}.3^{13}.\left(3-2\right)}\)
\(=\dfrac{2^5+1}{3-2}\)
\(=\dfrac{32+1}{1}=33\)
a, -7/2 + 3/4 - 17/2 = (-7/2 - 17/2) + 3/4 = -12 + 3/4 = -45/4 = -12,75.
b, -1/12 - 21/8 + 1/3 = -1/12 + 1/3 - 21/8 = 1/4 - 21/8 = -19/8 = -2,375
a: \(B=\frac12-\left\lbrack\frac38+\left(-\frac74\right)\right\rbrack\)
\(=\frac12-\frac38+\frac74\)
\(=\frac48-\frac38+\frac{14}{8}=\frac{15}{8}\)
b: \(-\frac{4}{12}-\left(-\frac{13}{39}-0,25\right)+0,75\)
\(=-\frac13+\frac13+0,25+0,75\)
=0,25+0,75
=1
c: \(\frac12-\frac13+\frac{1}{23}+\frac16\)
\(=\left(\frac12-\frac13+\frac16\right)+\frac{1}{23}\)
\(=\left(\frac16+\frac16\right)+\frac{1}{23}=\frac13+\frac{1}{23}=\frac{26}{69}\)
d: \(\left(-\frac{13}{7}-\frac49\right)-\left(-\frac{10}{7}-\frac49\right)\)
\(=-\frac{13}{7}-\frac49+\frac{10}{7}+\frac49\)
\(=-\frac{13}{7}+\frac{10}{7}=-\frac37\)
e: \(\left(\frac78-\frac52+\frac47\right)-\left(-\frac37+1-\frac{13}{8}\right)\)
\(=\frac78-\frac52+\frac47+\frac37-1+\frac{13}{8}\)
\(=\frac{20}{8}-\frac52=0\)
f: \(-\frac37+\left(3-\frac34\right)-\left(2,25-\frac{10}{7}\right)\)
\(=-\frac37+3-\frac34-2,25+\frac{10}{7}\)
\(=\frac77+0,75-\frac34\)
=1
g: \(\left(\frac53-\frac37+9\right)-\left(2+\frac57-\frac23\right)+\left(\frac87-\frac43-10\right)\)
\(=\frac53-\frac37+9-2-\frac57+\frac23+\frac87-\frac43-10\)
\(=\left(\frac53+\frac23-\frac43\right)+\left(-\frac37-\frac57+\frac87\right)+\left(9-2-10\right)\)
\(=\frac33+7-10=1-3=-2\)
\(\frac{10^3+2.5^3+5^3}{55}-\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)\(=\frac{2^3.5^3+2.5^3+5^3}{5.11}-\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{5^3\left(2^3+2+1\right)}{5.11}-\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{5^2.11}{11}-\frac{2.6}{3.5}=25-\frac{4}{5}=\frac{121}{5}\)
a: \(\frac{8^5\cdot\left(-5\right)^8+\left(-2\right)^5\cdot10^9}{2^{16}\cdot5^7+20^8}\)
\(=\frac{2^{15}\cdot5^8-2^5\cdot5^9\cdot2^9}{2^{16}\cdot5^7+\left(2^2\cdot5\right)^8}=\frac{2^{15}\cdot5^8-2^{14}\cdot5^9}{2^{16}\cdot5^7+2^{16}\cdot5^8}\)
\(=\frac{2^{14}\cdot5^8\left(2-5\right)}{2^{16}\cdot5^7\left(1+5\right)}=\frac{5}{2^2}\cdot\frac{-3}{6}=\frac54\cdot\frac{-1}{2}=-\frac58\)
b: \(\frac{\left(-0,25\right)^{-5}\cdot9^4\cdot\left(-2\right)^{-3}-2^{-2}\cdot6^9}{2^9\cdot3^6+6^6\cdot40}\)
\(=\frac{-2^{10}\cdot3^8\cdot\left(-\frac18\right)-\frac14\cdot2^9\cdot3^9}{2^9\cdot3^6+2^6\cdot3^6\cdot2^3\cdot5}=\frac{-2^7\cdot3^8-2^7\cdot3^9}{2^9\cdot3^6+2^9\cdot3^6\cdot5}\)
\(=\frac{-2^7\cdot3^8\left(1+3\right)}{2^9\cdot3^6\left(1+5\right)}=-\frac{1}{4\cdot3^2}\cdot\frac46=-\frac{1}{9\cdot6}=-\frac{1}{54}\)