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c) \(\frac{0,375-0,3+\frac{3}{11}+\frac{3}{12}}{0,625-0,5+\frac{5}{11}+\frac{5}{12}}=\frac{3\left(0,125-0,1+\frac{1}{11}+\frac{1}{12}\right)}{5\left(0,123-0,1+\frac{1}{11}+\frac{1}{12}\right)}=\frac{3}{5}\)
\(A=\left(\frac{3}{4}\right)^{-4}.\left(\frac{-2}{3}\right)^{-3}\)
\(A=\frac{256}{81}.\frac{-27}{8}\)
\(A=\frac{729}{64}\)
\(B=\left(4^3\right)^{-2}.a^{2015}\)
\(B=64^{-2}.a^{2015}\)
\(B=\frac{1}{4096}.a^{2015}\)
\(C=\left[\left(\frac{-1}{3}\right).\frac{2}{5}.\left(\frac{-3}{4}\right)\right]^3\)
\(C=\left[\frac{1}{10}\right]^3\)
\(C=\frac{1}{1000}\)
a. \(\frac{20^5.5^{10}}{100^5}\)
\(=\frac{20^5.\left(5^2\right)^5}{100^5}\)
\(=\frac{20^5.25^5}{100^5}\)
\(=\frac{500^5}{100^5}\)
\(=\left(\frac{500}{100}\right)^5\)
\(=5^5=3125\)
b. \(\frac{\left(0,9\right)^5}{\left(0,3\right)^6}\)
\(=\frac{\left(0,9\right)^5}{\left(0,3\right)^5.0,3}\)
\(=\left(\frac{0,9}{0,3}\right)^5.\frac{1}{0,3}\)
\(=3^5.\frac{1}{0,3}\)
\(=810\)
c. \(\frac{6^3+3.6^2+3^3}{-13}\)
\(=\frac{\left(3.2\right)^3+3.\left(3.2\right)^2+3^3}{-13}\)
\(=\frac{3^3\left(2^3+2^2+1\right)}{-13}\)
\(=\frac{3^3.13}{-13}\)
\(=\left(-3\right)^3\)
\(=-27\)
A = (1 - 2/3 + 4/3) - (4/5 - 1) + (7/5 + 2)
A= (3/3 - 2/3 + 4/3) - (4/5 - 5/5) + (7/5 + 10/5)
A= 5/3 + 1/5 + 17/5
A= 5/3 +18/5
A= 25/15 + 54/15
A= 79/15
B= (-3 + 3/4 - 1/3 ) : (5 + 2/5 - 2/3)
B= (-36/12 + 9/12 - 4/12) : (75/15 + 6/15 - 10/15)
B= -31/12 : 71/15
B= -155/284
C= (3/5 - 4/5 ) . (2/7 - 3/14) - (5/9 - 7/27) . (1 - 3/5) + (1 - 11/12) . (1-11/12)
C= -1/5 . 1/14 - 8/27 . 2/5 + 1/12 . 1/12
C=-1/70 - 16/135 + 1/144
C=-216/15120 - 1792/15120 + 105/15120
C=-1903/15120
\(\left(\frac{4}{9}+\frac{1}{3}\right)^2=\left(\frac{4}{9}+\frac{3}{9}\right)^2=\left(\frac{7}{9}\right)^2=\frac{49}{81}\)
\(\left(\frac{1}{2}-\frac{3}{5}\right)^3=\left(\frac{5}{10}-\frac{6}{10}\right)^3=\left(\frac{-1}{10}\right)^3=\frac{-1}{1000}\)
\(\left(\frac{-1}{5}\right)^5.\left(\frac{-6}{5}\right)^4=\frac{-5}{3125}.\frac{1296}{625}=\frac{-1296}{390625}\)
\(\left(\frac{3}{4}\right)^3:\left(\frac{3}{4}\right)^2:\left(-\frac{2}{5}\right)^3=\frac{3}{4}:\frac{-8}{125}=\frac{3}{4}.\frac{-125}{8}=\frac{-375}{32}\)
.
\(=\dfrac{\left(-5\right)\cdot0.81}{\left(\dfrac{5}{2}\right)^4\cdot\left(-\dfrac{10}{3}\right)^3\cdot\left(-1\right)}=\dfrac{-5\cdot0.81}{\dfrac{5^4\cdot10^3}{2^4\cdot3^3}}\)
\(=-4.05:\dfrac{5^7}{3^3\cdot2}=\dfrac{-81}{20}\cdot\dfrac{3^3\cdot2}{5^7}=\dfrac{-3^7\cdot2}{2^2\cdot5^8}=\dfrac{-3^7}{2\cdot5^8}\)