a: $2^6\cdot 3^3={\left(2^2\cdot 3\right)}^3={12}^3$

b: $6^4\cdot 8^3=2^4\cdot 3^4\cdot 2^9=2^{13}\cdot 3^4$

c: $16\cdot 81={36}^2$

d: ${25}^4\cdot 2^8={100}^4$

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)5^26=5^13.2=10^13

10^13x4^13=40^13

b)27^15=(3^3)^15+3^45

9^10=(3^2)^10=3^20

3^20x3^45=3^65

c)5^12=5^3.4=(5^4)^3=625^3

0,125^3.625^3=625,125^3

d)0,375^40=0,375^2.20=(0.375^2)^20=0,750^20

9^20:0,750^20=1.0012^20

k me

a)10⁸.2⁸=(10.2)⁸=20⁸

b)10⁸:2⁸=(10:2)⁸=5⁸

c)25⁴.2⁸=(5²)⁴.2⁸=5^2.4.2⁸=5⁸.2⁸=(5.2)⁸=10⁸

a. 10 mũ 8 . 2 mũ 8 = 10 . 2 mũ 8 = 20 mũ 8

b. 10 mũ 8 : 2 mũ 8 = 10 : 2 mũ 8 = 5 mũ 8

c . 25 mũ 4 . 2 mũ 8 = 390625 . 64 = 25000000

Bài 8:

a: \(\left(\dfrac{2}{5}+\dfrac{3}{4}\right)^2=\left(\dfrac{8+15}{20}\right)^2=\left(\dfrac{23}{20}\right)^2=\dfrac{529}{400}\)

b: \(\left(\dfrac{5}{4}-\dfrac{1}{6}\right)^2=\left(\dfrac{15}{12}-\dfrac{2}{12}\right)^2=\left(\dfrac{13}{12}\right)^2=\dfrac{169}{144}\)

viết bằng công thức ở chỗ \(\sum\) đi bạn

Bạn bảo cái gì cơ

a)\(\left(\frac{1}{5}\right)^{10}.5^{20}=\left(\frac{1}{5}\right)^{10}.5^{10.2}=\left(\frac{1}{5}\right)^{10}.25^{10}=\left(\frac{1}{5}.5\right)^{10}=1^{10}=1\)

b)\(5^2.3^5.\left(\frac{3}{5}\right)^2=\left(\frac{3}{5}.5\right)^2.3^5=3^2.3^5=3^7\)

c)\(\left(\frac{1}{16}\right)^3:\left(\frac{1}{8}\right)^2=\left(\frac{1}{8}\right)^{2.3}:\left(\frac{1}{8}\right)^2=\left(\frac{1}{8}\right)^{6+2}=\left(\frac{1}{8}\right)^8\)

\(a.\left(\frac{1}{5}\right)^{10}.5^{20}=\left(\frac{1}{5}\right)^{10}.5^{10.2}=\left(\frac{1}{5}\right)^{10}.\left(5^2\right)^{10}=\left(\frac{1}{5}\right)^{10}.25^{10}=\left(\frac{1}{5}.25\right)^{10}=5^{10}.\)

\(b.5^2.3^5.\left(\frac{3}{5}\right)^2=\left[5^2.\left(\frac{3}{5}\right)^2\right].3^5=\left(5.\frac{3}{5}\right)^2.3^5=3^2.3^5=3^7\)\(c.\left(\frac{1}{16}\right)^3:\left(\frac{1}{8}\right)^2=\left[\left(\frac{1}{4}\right)^2\right]^3:\left[\left(\frac{1}{2}\right)^3\right]^2=\left(\frac{1}{4}\right)^6:\left(\frac{1}{2}\right)^6=\left(\frac{1}{4}:\frac{1}{2}\right)^6=\left(\frac{1}{2}\right)^6\)

giải hộ mik vs mọi người ơi

sao khong ai tra loi het  z troi - .-

3^x*5^x-1=224

3^x*5^x/5=224

15^x=224*5

15^x=1120

=>ko tồn tại x thỏa mãn đề bài vị 15^x luôn có tận cùng bằng 5 (x khác 0 ) hoặc 1 ( x=0) ma 1120 co tận cùng bằng 0