a, x^7. x^3= x^10

b, (x^2)^5=x^10

c, x^12: x^2= x^10

\(2^5.8^4=2^5.\left(2^3\right)^4=2^5.2^{12}=2^{17}\)

\(25^6.125^3=\left(5^2\right)^6.\left(5^3\right)^3=5^{12}.5^9=5^{21}\)

1- 2x2x2x2x2

2-8x8x8x8

3- 25x25x25x25x25x25

4- 125x125x125

  \(2^5.8^4\)

\(=2^5.\left(2^3\right)^4\)

\(=2^5.2^{12}=2^{17}\)

  \(25^6.125^3\)

\(=\left(5^2\right)^6.\left(5^3\right)^3\)

\(=5^{12}.5^9=5^{21}\)

A=2²+2²+2³+2⁴+.........+2²⁰⁰⁵

^{\(2A=2^3+2^3+2^4+2^5+...+2^{2006}\)}

^{\(2A-A=\left(2^3+2^3+2^4+2^5+...+2^{2006}\right)-\left(2^2+2^2+2^3+2^4+...+2^{2005}\right)\)}

^{\(A=\left(2^{2006}+2^3\right)-\left(2^2+2^2\right)\)}

^{\(A=\left(2^{2006}+2^3\right)-2^3\)}

^{\(A=2^{2006}\)}

\(A=2^2+2^2+2^3+2^4+...+2^{2005}\)

\(\Rightarrow2A=2^3+2^3+2^4+2^5+...+2^{2005}+2^{2006}\)

\(\Rightarrow2A-A=\left(2^3+2^3+2^4+2^5+...+2^{2006}\right)-\left(2^2+2^2+2^3+2^4+...+2^{2005}\right)\)

Triệt tiêu hai vế \(\Rightarrow A=\left(2^{2006}+2^3\right)-\left(2^2+2^2\right)=2^{2006}+2^3-2^3\)

\(\Rightarrow A=2^{2006}\)

a) \(3^5.4^5=\left(3.4\right)^5=12^5\)

b) \(8^5.2^3=\left(2^3\right)^5.2^3=2^{15}.2^3=2^{15+3}=2^{18}\)

\(3^5.4^5=3+4^5=7^5\)

\(8^5.2^3=8+2^{5+3}=10^8\)

Ko biết nữa !

a, 12⁵

b, 2¹⁸

Hok tốt

\(1=1^3\)

\(3+5=8=2^3\)

\(7+9+11=27=3^3\)

\(13+15+17+19=64=4^3\)

\(21+23+25+27+29=125=5^3\)

A. (-5) ².(-5)⁷

⁼ (-5) ⁽²⁺⁷⁾

= (-5)⁹

B. (0.75)³ :0,75

= (0.75)^(3-1)

= (0.75)²

B. 0,2¹⁰ :0,2⁷

= 0,2^(10-7)

= 0,2³