-4^3.(-5)^2

(-4).(-4).(-4).(-5).(-5).(-5) = (-4)3.(-5)3 = 203

\(a,=5^{40}\cdot5^{12}=5^{52}\\ b,=x^{7+4+3}=x^{14}\\ c,=\left(3\cdot4\right)^6=12^6\)

a) \(25^{20}.125^4=\left(5^2\right)^{20}.\left(5^3\right)^4=5^{40}.5^{12}=5^{40+12}=5^{52}\)

b) \(x^7.x^4.x^3=x^{7+4+3}=x^{14}\)

c) \(3^6.4^6=\left(3.4\right)^6=12^6\)

Anh đã từng làm em hi!

\(\begin{array}{l}{3^3}{.3^4} = {3^{3 + 4}} = {3^7};\\{10^4}{.10^3}  = 10^{4+3}= {10^7};\\{x^2}.{x^5} = x^{2+5} = {x^7}.\end{array}\

\(a,\left(-7\right)^6\)
\(b,\left(-4\right)^3.\left(-5\right)^3=\left[\left(-4\right).\left(-5\right)\right]^3=20^3\)

4 mũ 25

\(\frac{4}{9}x^4-16x^2=\left(\frac{2}{3}x^2\right)^2-\left(4x\right)^2=\left(\frac{2}{3}x^2+4x\right).\left(\frac{2}{3}x^2-4x\right)\)

4 . 4² . 4³ . ... . 4⁹⁹ . 4¹⁰⁰ 

= 4^{1 + 2 + 3 + ... + 99 + 100}

Ta có : 

1 + 2 + 3 + ... + 100

= (1 + 100) + (2 + 99) + ... + (50 + 51)             (Có : 100 : 2 = 50 số)

= 101 + 101 + ... + 101                                   (Có 50 số)

= 101 x 50

= 5050

Vậy 4^{1 + 2 + 3 + ... + 99 + 100} = 4⁵⁰⁵⁰

4 . 4² . 4³ . ... . 4⁹⁹ . 4¹⁰⁰ 

= 4^{1 + 2 + 3 + ... + 99 + 100}

Ta có : 

1 + 2 + 3 + ... + 100

= (1 + 100) + (2 + 99) + ... + (50 + 51)             (Có : 100 : 2 = 50 số)

= 101 + 101 + ... + 101                                   (Có 50 số)

= 101 x 50

= 5050

Vậy 4^{1 + 2 + 3 + ... + 99 + 100} = 4⁵⁰⁵⁰

Đúng thì k nha !!!