\(a)9.4.25.8.125\)

\(=9.\left(4.25\right).\left(8.125\right)\)

\(=9.100.1000\)

\(=900.1000\)

\(=900000\)

\(a,9.4.25.8.125=9.\left(4.25\right).\left(8.125\right)=9.100.1000=900000\)

\(b,25.5.27.2\)(câu này hình như thiếu đề, ko tính nhanh đc)

\(c,37.7+80.3+43.7\)\(=7.\left(37+43\right)+80.3\)\(=7.80+3.80=80\left(7+3\right)=80.10=800\)

\(d,113.38+113.62+87.62+87.38\)\(=113\left(38+62\right)+87\left(62+38\right)\)

\(=113.100+87.100=100.\left(113+87\right)=100.200=20000\)

Viết gọn lũy thừa:

\(a,x.x.y.y.x.y.x=\left(x.x.x.x\right).\left(y.y.y\right)=x^4.y^4\)

\(b,7^5:343=7^5:7^3=7^{5-3}=7^2\)

\(c,A^{12}:A^{18}=A^{12-18}=A^{-6}\)

\(d,x^7.x^4.x=x^{7+4+1}=x^{12}\)

(3x - 6).3 = 3⁴

3x - 6 = 3⁴ : 3

3x - 6 = 3³

3x - 6 = 27

3x = 27 + 6

3x  =33

x = 33:3

x=11

12x - 34 = 3².3⁵

12x - 34 = 3⁷

12x - 34 = 2187

12x = 2187 + 34

12x = 2221

x = 2221:12

x=2221/12

a) x⁸ : x² = 16

x⁶ = 16 = ... ( chỗ này bn xem có số nào mũ 6 = 16 ko nha)

...

b) x³.x².x^-4 = 60

x^3+2-4 = 60

x^-1 = 60 = (1/60)^-1

=> x = 1/60

2 bài đề sai rồi

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

2a⁴+4a²+2=2a⁴+2a²+2a²+2=2a²(a²+1)+2(a²+1)=(a²+1)(2a²+2)=2(a²+1)²

x²+4x+3x+12=x(x+3)+4(x+3)=(x+4)(x+3)

1)1/9 x 3^x = 2187:81=27

            3^x=27:1/9=243=3⁵

            =>x=5

\(\frac{1}{9}.3^4.3^x=3^7\)

\(\Leftrightarrow3^x=3^7:\frac{1}{9}:3^4=243\)

\(\Leftrightarrow3^x=3^5\)

\(\Leftrightarrow x=5\)