a) \(\dfrac{1}{2}.\dfrac{1}{-3}+\dfrac{1}{-3}.\dfrac{1}{4}+\dfrac{1}{4}.\dfrac{1}{-5}+\dfrac{1}{-5}.\dfrac{1}{6}\)

\(=\dfrac{1}{-3}\left(\dfrac{1}{2}+\dfrac{1}{4}\right)+\dfrac{1}{-5}\left(\dfrac{1}{4}+\dfrac{1}{6}\right)\)

\(=\dfrac{1}{-3}.\dfrac{3}{4}+\dfrac{1}{-5}.\dfrac{5}{12}\)

\(=\left(-\dfrac{1}{4}\right)+\left(-\dfrac{1}{12}\right)\)

\(=-\dfrac{1}{3}\)

b) \(A=\dfrac{81^4.3^{10}.27^5.3^{12}}{3^{18}.9^3.243^2}\)

\(=\dfrac{9^8.9^8.9^{13}.9^{10}}{9^{16}.9^3.9^3}\)

\(=\dfrac{9^{39}}{9^{22}}\)

\(=9^{17}\)

\(A=\dfrac{81^4\cdot3^{10}\cdot27^5\cdot3^{12}}{3^{18}\cdot9^3\cdot243^2}=\dfrac{3^{16}\cdot3^{10}\cdot3^{15}\cdot3^{12}}{3^{18}\cdot3^6\cdot3^{10}}=\dfrac{3^{53}}{3^{34}}=3^{19}\)

Vậy A = 3¹⁹

Ngân Hà làm đúng phần a) nhưng làm sai phần b) nên mk chỉ làm phần b) thôi

\(A=\frac{81^4.3^{10}.27^5:3^{12}}{3^{18}:9^3.243^2}=\frac{3^{16}.3^{10}.3^{15}:3^{12}}{3^{18}:3^6.3^{10}}=\frac{3^{29}}{3^{22}}=3^7\)

\(B=\frac{2.55^2-9.55^{21}}{25^{10}}:\frac{5\left(3.7^{15}-19.7^{14}\right)}{7^{16}+3.7^{15}}=\frac{2.55^2-9.55^2.55^{19}}{25^{10}}:\frac{5\left(21.7^{14}-19.7^{14}\right)}{7.7^{15}+3.7^{15}}=\frac{55^2\left(55^{19}.9-2\right)}{25^{10}}:\frac{5.7^{14}.2}{7^{15}.10}=\frac{55^2\left(55^{19}.9-2\right)}{25^{10}}.\frac{7^{15}.10}{5.7^{14}.2}\)Chịu ==

\(1.\dfrac{27^4.4^3}{9^5.8^2}=\dfrac{3^{12}.2^6}{3^{10}.2^6}=3^2=9\)

\(2.\dfrac{8^5.3^{15}}{2^{14}.81^4}=\dfrac{2^{15}.3^{15}}{2^{14}.3^{16}}=\dfrac{2}{3}\)

Ý 1:

\(\dfrac{27^4.4^3}{9^5.8^2}=\dfrac{\left(3^3\right)^4.\left(2^2\right)^3}{\left(3^2\right)^5.\left(2^3\right)^2}=\dfrac{3^{12}.2^6}{3^{10}.2^6}=3^2=9\)

Ý 2:

\(\dfrac{8^5.3^{15}}{2^{14}.81^4}=\dfrac{\left(2^3\right)^5.3^{15}}{2^{14}.\left(3^4\right)^4}=\dfrac{2^{15}.3^{15}}{2^{14}.3^{16}}=\dfrac{2^{14}.2.3^{15}}{2^{14}.3^{15}.3}=\dfrac{2}{3}\)

a: \(=\dfrac{2^4\cdot3^6\cdot2\cdot3}{2^4\cdot3^6}=6\)

b: \(=\dfrac{2^{20}\cdot3^{20}}{2^{18}\cdot3^{18}}=2^2\cdot3^2=36\)

c: \(=\dfrac{12^5\cdot13}{12^6\cdot13}-\dfrac{12^8\cdot\left(-11\right)}{12^9\cdot\left(-11\right)}=\dfrac{1}{12}-\dfrac{1}{12}=0\)

\(=>M=\dfrac{2^{28}.3^{18}.5-2^{29}.3^{20}}{2^{28}.3^{19}.5-2^{29}.3^{18}.7}\)

\(=\dfrac{2^{28}.3^{18}\left(5-2.3^2\right)}{2^{28}.3^{18}\left(3.5-2.7\right)}\)

\(=5-2.3^2\)

\(=5-2.9\)

\(=5-18\)

\(=-13\)

\(#Nzgoca\)

Lời giải:

Gọi biểu thức là $A$

\(A=\frac{2^{10}.3^8+5.(2^2)^5.3^8}{2^{10}.(3^3)^3-2^{10}.(3^2)^4}=\frac{2^{10}.3^8+5.2^{10}.3^8}{2^{10}.3^9-2^{10}.3^{8}}\)

\(=\frac{2^{10}.3^8(1+5)}{2^{10}.3^8(3-1)}=\frac{6}{2}=3\)

Bài 1: Tìm số đối.

- Số đối của \(\dfrac{1}{2}\) là \(-\dfrac{1}{2}\)

- Số đối của \(-\dfrac{3}{4}\) là \(\dfrac{3}{4}\)

- Số đối của \(\dfrac{7}{-12}\) là \(\dfrac{7}{12}\)

Bài 2: Thu gọn:

\(\dfrac{2^4.3^3-2^4.3^3}{2^5.3^4-2^6.3^3}=\dfrac{0}{2^5.3^4-2^6.3^3}=0\)

1.Tìm số đối:

số đối của 1/2 là |1/2| = 1/2

số đối của -3/4 là |-3/4|=3/4

số đối của 7/-12 là |7/-12|=7/12

2. Thu gọn

(2^4.3^3-2^4.3^3)/(2^5.3^4-2^6.3^3)

=0/(2^5.3^4-2^6.3^3)

=0

like cho mình nhé

sự like của bạn là niềm vinh hạnh của mình

\(A=\dfrac{12^{15}\cdot3^4-4^5\cdot3^9}{27^3\cdot2^{10}-32^3\cdot3^9}\\ =\dfrac{\left(2^2\cdot3\right)^{15}\cdot3^4-\left(2^2\right)^5\cdot3^9}{\left(3^3\right)^3\cdot2^{10}-\left(2^5\right)^3\cdot3^9}\\ =\dfrac{2^{30}\cdot3^{15}\cdot3^4-2^{10}\cdot3^9}{3^9\cdot2^{10}-2^{15}\cdot3^9}\\ =\dfrac{3^9\cdot2^{10}\left(2^{20}\cdot3^{10}\right)}{3^9\cdot2^{10}\left(1-2^5\right)}\\ =\dfrac{\left(2^2\right)^{10}\cdot3^{10}}{1-32}\\ =\dfrac{\left(2^2\cdot3\right)^{10}}{-31}\\ =\dfrac{-12^{10}}{31}\)

\(B=\dfrac{3}{1^2\cdot2^2}+\dfrac{5}{2^2\cdot3^2}+...+\dfrac{99}{49^2\cdot50^2}\\ =\dfrac{2^2-1^2}{1^2\cdot2^2}+\dfrac{3^2-2^2}{2^2\cdot3^2}+...+\dfrac{50^2-49^2}{49^2\cdot50^2}\\ =\dfrac{1}{1^2}-\dfrac{1}{2^2}+\dfrac{1}{2^2}-\dfrac{1}{3^2}+...+\dfrac{1}{49^2}-\dfrac{1}{50^2}\\ =1-\dfrac{1}{2500}\\ =\dfrac{2499}{2500}\)

=\(\frac{2^{30}3^{16}.5^{50}.7+2^{30}.3^{15}.3^2.11.5^{48}}{11.2^{25}.2^4.5^4.3^{18}.5^{18}.5^{30}-2^{30}.5^{30}.5^{22}.3^{18}}\)

=\(\frac{2^{30}.3^{16}.5^{50}.7+2^{30}.3^{17}.11.5^{48}}{11.2^{29}.5^{52}.3^{18}-2^{30}.5^{52}.3^{18}}\)

=\(\frac{2^{30}.3^{16}.5^{48}.11\left(5^2.7+3\right)}{2^{29}.5^{52}.3^{18}.11\left(1-2\right)}\)

=\(\frac{2.\left(5^2.7+3\right)}{5^4.3^2\left(1-2\right)}\)

=\(\frac{2.178}{5^4.3^2.\left(-1\right)}\)

=\(\frac{356}{-5625}\)

Hk tốt