Bài làm:

Ta có: \(\frac{9^2.\left(-4\right)^5.72}{5.\left(-6\right)^6}\cdot\frac{6^3.81.\left(-4\right)}{\left(-8\right)^6.3^9}\)

\(=\frac{3^2.-2^{10}.2^3.3^2.2^3.3^3.3^4.-2^2}{5.2^3.3^3.2^{18}.3^9}\)

\(=\frac{2^{18}.3^{11}}{2^{21}.3^{12}.5}\)

\(=\frac{1}{2^3.2.5}=\frac{1}{120}\)

\(\frac{25^5.2^{10}}{20^4.5^4}\)

=\(\frac{25^5.2^{10}}{20^4.25^2}\)

=\(\frac{25^3.2^{10}}{20^4}\)

=\(\frac{25^3.1024}{160000}\)

=\(\frac{25^3.4}{25^2}\)

=\(25.4\)

=100

#)Giải :

\(9^8:\left(27^3.81^2\right)=\left(3^2\right)^8:\left[\left(3^3\right)^3.\left(3^4\right)^2\right]=3^{16}:\left[3^9.3^8\right]\)

Đến đây ez rùi ^^

9⁸:(27³.81²) = 9⁸:(3^3x3.3^4x2)=9⁸:3¹⁷= \(\frac{1}{3^9}\)

a: ta có: \(5\cdot8^{12}\cdot9^5\cdot\left(-3\right)^2\cdot\left(-16\right)^5\)

\(=5\cdot\left(2^3\right)^{12}\cdot\left(3^2\right)^5\cdot3^2\cdot\left(-1\right)\cdot2^{20}\)

\(=-5\cdot3^{12}\cdot2^{56}\)

Ta có: \(7\cdot49^3\cdot81^5\cdot\left(-7\right)^{10}\cdot\left(-8\right)^5\)

\(=-7\cdot\left(7^2\right)^3\cdot\left(3^4\right)^5\cdot7^{10}\cdot\left(2^3\right)^5\)

\(=-7\cdot7^6\cdot3^{20}\cdot7^{10}\cdot2^{15}=-7^{17}\cdot2^{15}\cdot3^{20}\)

Ta có: \(B=\frac{5\cdot8^{12}\cdot9^5\cdot\left(-3\right)^2\cdot\left(-16\right)^5}{7\cdot49^3\cdot81^5\cdot\left(-7\right)^{10}\cdot\left(-8\right)^5}\)

\(=\frac{-5\cdot3^{12}\cdot2^{56}}{-7^{17}\cdot2^{15}\cdot3^{20}}=\frac{5\cdot2^{41}}{7^{17}\cdot3^8}\)

b: \(13\cdot4^7\cdot9^{15}-9^7\cdot\left(-16\right)^4\)

\(=13\cdot2^{14}\cdot3^{20}-3^{14}\cdot2^{16}\)

\(=3^{14}\cdot2^{14}\left(13\cdot3^6-2^2\right)\)

\(15\cdot3^{12}\cdot2^8+3\cdot27^5\cdot\left(-8\right)^{10}\)

\(=3\cdot5\cdot3^{12}\cdot2^8+3\cdot\left(3^3\right)^5\cdot\left(2^3\right)^{10}=3^{13}\cdot5\cdot2^8+3^{16}\cdot2^{30}\)

\(=3^{13}\cdot2^8\left(5+3^3\cdot2^{22}\right)\)
Ta có: \(C=\frac{13\cdot4^7\cdot9^{15}-9^7\cdot\left(-16\right)^4}{15\cdot3^{12}\cdot2^8+3\cdot27^5\cdot\left(-8\right)^{10}}\)

\(=\frac{3^{14}\cdot2^{14}\left(13\cdot3^6-2^2\right)}{3^{13}\cdot2^8\left(5+3^3\cdot2^{22}\right)}=\frac{3\cdot2^6\cdot\left(13\cdot3^6-2^2\right)}{5+3^3\cdot2^{22}}\)

a) \(9^8=\left(3^2\right)^8=3^{16}\)

\(27^3=\left(3^3\right)^3=3^9\)

\(81^2=\left(3^4\right)^2=3^8\)

\(\Leftrightarrow3^{16}:\left(3^9.3^8\right)\)

\(\Leftrightarrow3^{16}:3^{17}\)

\(\Leftrightarrow3^{-1}=\frac{1}{3}\)

a) 9^́́́8 : ̣(27³ . 81²)= 3^{16  :} 3⁹ . 3⁸ = 3¹⁵

a)  76.12 + 24.12 - 200

= 12.(76+24)-200

= 12.100 -200

= 1200-200 = 1000

b) 3^4 . 36 + 4^3 . 81 -100

= 81.36 + 64.81 -100

= 81.(36+64)-100

=81.100-100

=8100-100 = 8000

a)  76.12 + 24.12 - 200

= 12.( 76+24 ) - 200

= 12.100 - 200

= 1200 - 200 = 1000

b) 3^4 . 36 + 4^3 . 81 - 100

= 81.36 + 64.81 - 100

= 81.(36+64) - 100

=81.100 - 100

=8100 - 100 = 8000

Học tốt!

\(\frac{27^2.8^5}{6^6.32^3}=\frac{\left(3^3\right)^2.\left(2^3\right)^5}{2^6.3^6.\left(2^5\right)^3}\)

               \(=\frac{3^6.2^{15}}{2^6.3^6.2^{15}}\)

                \(=\frac{1}{2^6}\)

Chú ý : Bạn nào làm nhanh , đấy đủ và đúng thì minh mới k cho đó nha

bn có 0 đ mà k cho ng` khác cũng chẳng có ích j đâu

\(3^3\times9^3\times81\)

\(=3^{\text{3}}\times\left(3^2\right)^3\times9^2\)

\(=3^3\times3^6\times3^4=3^{13}\)

\(3^3\).\(3^6\).\(3^4\)

=\(3^{13}\)