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( 27 - 11 ) + ( 20 - 9 - 27 )
= 27 - 11 + 20 - 9 - 27
= (27 - 27) + 20 - (11 + 9)
= 20 - 20 = 0
\(\frac{9^3\cdot2^{10}\cdot27^5}{4^5\cdot81^6}=\frac{3^6\cdot2^{10}\cdot3^{15}}{2^{10}\cdot3^{24}}=\frac{1}{3^3}=\frac{1}{27}\)
\(\frac{27^4\cdot2^5-3^{11}\cdot4^3}{8^2\cdot9^6}=\frac{3^{12}\cdot2^5}{2^6\cdot3^{12}}-\frac{3^{11}\cdot2^6}{2^6\cdot3^{12}}=\frac{1}{2}-\frac{1}{3}=\frac{1}{6}\)
=))
a) \(\frac{9^3.2^{10}.27^5}{4^5.81^6}\)= \(\frac{\left(3^2\right)^3.2^{10}.\left(3^3\right)^5}{\left(2^2\right)^5.\left(3^4\right)^5}\)= \(\frac{3^{2.3}.2^{10}.3^{3.5}}{2^{2.5}.3^{4.5}}\)= \(\frac{3^6.2^{10}.3^{15}}{2^{10}.3^{20}}\)= \(\frac{3^{21}.2^{10}}{2^{10}.3^{20}}\)= \(\frac{3^{20}.2^{10}.3}{2^{10}.3^{20}}\)= \(3\)
a, (-25) .68 + (-34).(-250)
= -1700 + 8500
= 6800
b, 7.5 + 9 . [(-3) - (-27)]
= 16.5 . 24
= 396
a) -175 - ( -7 . 5^2 + 4 . 2^3)
= -175 - ( -175 + 32 )
= -175 - -175 +32
= 0 +32
= 32
b) (-27) + 20 + (-9) + 27 + (-11)
= (-27 + 27 ) + 20 + (-11) + (- 9)
= 0 + 9 + (-9)
= 0 + 0
= 0