7.6^10.2^20.3^6-2^19.6^15/9.6^19.2^9-4.3^17.2^26

\(27^3.9^4.243=3^{3.3}.3^{2.4}.3^5\)

\(3^9.3^8.3^5=3^{22}\)

\(25^3.125^2=5^{2.3}.5^{3.2}=5^6.5^6=5^{12}\)

= 3^6 - 4 x 3 + 5^8 x 5^0 : 25^2

= 729 - 12 + 5^8 x 5^0 : 5^4

= 729 - 12 + 5^4

= 729 - 12 + 625

= 717 + 625

= 1342

bằng 0

Bài 1:

a) \(8^5\cdot8^2=8^7\)

b) \(9^3\cdot3^2=\left(3^2\right)^3\cdot3^2=3^6\cdot3^2=3^8\)

c) \(2^7\cdot5^7=10^7\)

d) \(27^6:3^3=\left(3^3\right)^6:3^3=3^{18}:3^3=3^{15}\)

Bài 2:

a) \(x^6:x^3=125\)

\(\Rightarrow x^3=125\)

\(\Rightarrow x=5\)

b) \(x^{20}=x\)

\(\Rightarrow x^{20}-x=0\)

\(\Rightarrow x\left(x^{19}-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x^{19}-1=0\Rightarrow x=1\end{matrix}\right.\)

c) \(3^x\cdot3=243\)

\(\Rightarrow3^x=81\)

\(\Rightarrow x=4\)

d) \(2x-138=2^3\cdot3^2\)

\(\Rightarrow2x-138=72\)

\(\Rightarrow2x=200\)

\(\Rightarrow x=100\)

Giải:

Bài 1:

a) \(8^5.8^2=8^{5+2}=8^7\)

b) \(9^3.3^2=3^6.3^2=3^{6+2}=3^8\)

c) \(2^7.5^7=\left(2.5\right)^7=10^7\)

d) \(27^6:3^3=3^{18}:3^3=3^{18-3}=3^{15}\)

Bài 2:

a) \(x^6:x^3=x^{6-3}=x^3=125\)

\(\Leftrightarrow x=5\)

b) \(x^{20}=x\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\\x=1\end{matrix}\right.\)

c) \(3^x.3=243\)

\(\Leftrightarrow3^{x+1}=243\)

\(\Leftrightarrow3^{x+1}=3^5\)

\(\Leftrightarrow x+1=5\Leftrightarrow x=4\)

d) \(2.x-138=2^3.3^2\)

\(\Leftrightarrow2.x-138=8.9\)

\(\Leftrightarrow2.x-138=72\)

\(\Leftrightarrow2.x=72+138\)

\(\Leftrightarrow2.x=210\Leftrightarrow x=105\)

Chúc bạn học tốt!

Bài làm :

\(2^3.4.256\)

\(=2^3.2^2.2^8\)

\(=2^{13}\)

\(2^3\).\(2^2\).\(2^8\)=\(2^{3+2}\).\(2^8\)=\(2^5\).\(2^8\)=\(2^{5+8}\)=\(2^{13}\)

7² - 7 . ( 13 . x ) =14

 => 49 - 7.( 13.x) = 14

 => 7.(13.x) = 49 -14 = 35

 => 13.x = 35 : 7 = 5

 => x = 5 : 13

 => x = 5/13 

9 x 5⁵ : ( 5⁷ : 5⁴ ) + 2³ x 5

= 9 x 5⁵ : 5³ + 8 x 5

= 9 x 5² + 40

= 225+40

= 265