a) \(\frac{75^3.3^7}{81^4.5^6}=\frac{5^3.3^3.5^3.3^7}{\left(3^4\right)^4.5^6}=\frac{5^6.3^3.3^7}{3^{16}.5^6}=\frac{3^{10}}{3^{16}}=\frac{1}{3^6}=\frac{1}{729}\)
b) \(\frac{6^6.4^2}{3^{12}.2^8}=\frac{2^6.3^6.\left(2^2\right)^2}{3^{12}.2^8}=\frac{2^6.3^6.2^4}{3^{12}.2^8}=\frac{2^{10}.3^6}{3^{12}.2^8}=\frac{2^2.1}{3^6}=\frac{4}{729}\)
c) \(\frac{34^5.2^5}{2^{14}.17^5}=\frac{2^5.17^5.2^5}{2^{14}.17^5}=\frac{2^{10}}{2^{14}}=\frac{1}{2^4}=\frac{1}{16}\)

 1/2 x 2 mũ n cộng 4 x 2 mũ n = 9 x 2 mũ n

\(a=4^5.9^4-2.\dfrac{6^9}{2^{10}}.3^8+6^8.20\)

Đề là như vầy đúng ko bn?

[6⁸.(-4)³]/(9⁴.12⁶)

= (-2⁸.3⁸.2⁶)/(3⁸.2⁶.3⁶)

= -(2¹⁴.3⁸)/(2⁶.3¹⁴)

= - 2⁸/3⁶

= -256/729

12 mũ 5 nhân 9 mũ 6 phần 27 mũ 5 nhân 2 mũ 12

\(\dfrac{27^4\cdot\left(-8\right)^2}{9^5\cdot6^3}=\dfrac{\left(3^3\right)^4\cdot\left(2^3\right)^2}{\left(3^2\right)^5\cdot\left(2\cdot3\right)^3}=\dfrac{3^{12}\cdot2^6}{3^{10}\cdot2^3\cdot3^3}=\dfrac{2^3}{3}=\dfrac{8}{3}\)

\(\dfrac{24^4.\left(-8\right)^2}{9^5.6^3}\)

=\(\dfrac{\left(4.6\right)^4.\left(2^3\right)^2}{\left(3^2\right)^5.6^3}\)

=\(\dfrac{4^4.6^4.2^6}{3^{10}.6^3}\)

=\(\dfrac{2^{14}.6}{3^{10}}\)

a) 2 mũ 6 nhân 125 mũ 2 = 1000000 ( 1 triệu )

b) 27 mũ 4 chia 3 mũ 8 = 81

c) 18 mũ 8 nhân 9 mũ 4 = 7.2301961e+13 ( tính được nhưng dài )

d) 4 mũ 9 chia 5 mũ 27 = 3.5184372e-14 ( tính được nhưng dài )

a. 2⁶ . 125²

= (2³)² . 125²

= 8² . 125²

= (8.125)² = 1000²

b. 27⁴ : 3⁸

= (3³)⁴ : 3⁸

= 3¹² : 3⁸

= 3^12-8 = 3⁴

c. 18⁸ . 9⁴

= 18⁸ . (3²)⁴

= 18⁸ . 3⁸

= (18.3)⁸ = 54⁸

d. 4⁹ : 5²⁷

= 4⁹ : (5³)⁹

= 4⁹ : 125⁹

= (4 : 125)⁹ = (0,032)⁹

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