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?

$\textbf{A)}$

$\dfrac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}$

$=\dfrac{(2^2)^5(3^2)^4-2(2\cdot3)^9}{2^{10}\cdot3^8+2^2\cdot5(2\cdot3)^8}$

$=\dfrac{2^{10}3^8-2^{10}3^9}{2^{10}3^8+2^{10}\cdot5\cdot3^8}$

$=\dfrac{2^{10}3^8(1-3)}{2^{10}3^8(1+5)}$

$=\dfrac{-2}{6}$

$=-\dfrac{1}{3}.$

mình chịu

chịu thì vào đây chat lm j

dài vãi

Ta có:

$H=\dfrac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}$

$=\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}$

$=\dfrac{2^{12}\cdot3^{10}(1+5)}{2^{11}\cdot3^{11}(2\cdot3-1)}$

$=\dfrac{2^{12}\cdot3^{10}\cdot6}{2^{11}\cdot3^{11}\cdot5}$

$=\dfrac{2^2}{5}$

$=\dfrac45.$

[6⁸.(-4)³]/(9⁴.12⁶)

= (-2⁸.3⁸.2⁶)/(3⁸.2⁶.3⁶)

= -(2¹⁴.3⁸)/(2⁶.3¹⁴)

= - 2⁸/3⁶

= -256/729

\(\frac{2^{15}\cdot9^4}{6^6\cdot8^3}\)

\(=\frac{2^{15}\cdot3^8}{2^6\cdot3^6\cdot\left(2^3\right)^3}\)

\(=\frac{2^{15}\cdot3^8}{2^{15}\cdot3^6}=3^2=9\)