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\(\left(15.3^{42}-9^{20}\right):27^3\)
\(=\left(5.3.3^{42}-3^{40}\right):3^9\)
\(=\left(5.3^{43}-3^{40}\right):3^9\)
\(=3^{40}\left(5.3^3-1\right):3^9\)
\(=3^{31}\left(5.3^3-1\right)\)
\(=134.3^{31}\)
\(\left(15.3^{42}-9^{20}\right):27^3=15.3^{42}:27^3-9^{20}:27^3\\ \\ =15.3^{42}:\left(3^3\right)^3-9^{20}:9^3:3^3=15.3^{33}-\left(3^2\right)^{20}:\left(3^2\right)^3:3^3\)
\(=15.3^{33}-3^{40}:3^6:3^3=15.3^{33}-3^{31}\\ \\ =15.3^2.3^{31}-3^{31}=135.3^{31}-3^{31}\\ \\ =3^{31}.\left(135-1\right)=3^{31}.134\)
a) 13 . 58 . 4 + 32 . 26 . 2 + 52 . 10 b) 53 . 51 + 4 + 53 . 49 + 91 + 53
= 52 . 58 + 32 . 52 + 52 . 10 = 53 . 55 + 53 . 145 + 53 . 1
= 52. ( 58 + 32 + 10 ) = 53 . ( 55 + 145 + 1 )
= 52 . 100 = 53 . 201
= 52000 = 10653
~ Chúc bn hok tốt ~
\(\frac{4^8.3^{12}.27^2}{6^{12}.9^3}\)
= \(\frac{\left(2^2\right)^8.3^{12}.27^2}{\left(2.3\right)^{12}.\left(3^2\right)^3}\)
= \(\frac{2^{16}.3^{12}.27^2}{2^{12}.3^{12}.27^2}\)
= \(\frac{2^{16}}{2^{12}}\)= 24 = 16
25.(27-39)-27.(25-39)
=25x27-25x39-27x25-27x39
=(25x27-27x25)+27.39-25x39
=0+39(27-25)
=0+39x2
=78
\(x=\dfrac{4}{27}-\dfrac{2}{3}\)
\(x=-\dfrac{14}{27}\)
\(=27.\left(-53\right)+27.\left(-47\right)\\ =27.\left[\left(-53\right)+\left(-47\right)\right]\\ =27.-100\\ =-2700\)
-2700