a) (4x)² , (9x²y)² , 

b) (3ab⁴)³ , (\(-\frac{1}{5}\)x³y²)

\(a,=8\left(x^3-125\right)=8\left(x-5\right)\left(x^2+5x+25\right)\\ b,=\left(0,1+4x\right)\left(0,01-0,4x+16x^2\right)\\ c,=\left(x+\dfrac{1}{5}y\right)\left(x^2-\dfrac{1}{5}xy+\dfrac{1}{25}y^2\right)\\ d,=\left(3x-\dfrac{1}{2}y\right)\left(9x^2+\dfrac{3}{2}xy+\dfrac{1}{4}y^2\right)\\ e,=\left(x-1+3\right)\left[\left(x-1\right)^2-3\left(x-1\right)+9\right]\\ =\left(x+2\right)\left(x^2-2x+1-3x+3+9\right)\\ =\left(x+2\right)\left(x^2-5x+13\right)\\ f,=\left(\dfrac{x^2}{2}-y^2\right)\left(\dfrac{x^4}{4}+\dfrac{x^2y^2}{2}+y^4\right)\)

a: \(=2x^5\cdot2y^{12}\cdot4z^8\)

b: \(=4x^5y^{12}z^8+4x^5y^{12}z^8+5x^5y^{12}z^8+3x^5y^{12}z^8\)

a)
=(x-2)³
b)\(\left(2-x\right)^3\)
c)\(\left(x+\dfrac{1}{3}\right)^3\)
d)\(\left(\dfrac{x}{2}+y\right)^3\)
e)
\(=\left(x-1\right)^2\left(x-1-15\right)+25\left[3\left(x-1\right)-5\right]\)
\(=\left(x-1\right)^2\left(x-16\right)+25\left(3x-3-5\right)\)
\(=\left(x-1\right)^2\left(x-16\right)+25\left(3x-8\right)\)
 

Bài 1:

a: \(4\cdot64\cdot2^8\)

\(=2^2\cdot2^6\cdot2^8\)

\(=2^{2+6+8}=2^{16}\)

b: \(128\cdot27=2^7\cdot3^3\)

c: \(4\cdot27:\left(3^{11}\cdot\frac19\right)=4\cdot27:3^9=4\cdot\frac{3^3}{3^9}=\frac{4}{3^6}=\left(\frac{2}{3^3}\right)^2\)

Bài 2:

a: \(\left(\frac12\right)^3\cdot4+\frac34\)

\(=4\cdot\frac18+\frac34\)

\(=\frac48+\frac34=\frac48+\frac68=\frac{10}{8}=\frac54\)

b: Sửa đề: \(4^6\cdot\left(\frac12\right)^{12}\)

Ta có: \(4^6\cdot\left(\frac12\right)^{12}\)

\(=\left(2^2\right)^6\cdot\frac{1}{2^{12}}\)

\(=\frac{2^{12}}{2^{12}}=1\)

c: Ta có: \(\left(\frac12\right)^5-1,5^2\)

\(=\frac{1}{32}-\frac94\)

\(=\frac{1}{32}-\frac{72}{32}=\frac{-71}{32}\)

d: \(\frac{14^{16}\cdot35^7}{10^9\cdot7^{22}}\)

\(=\frac{7^{16}\cdot2^{16}\cdot7^7\cdot5^7}{2^9\cdot5^9\cdot7^{22}}\)

\(=\frac{7^{23}}{7^{22}}\cdot\frac{2^{16}}{2^9}\cdot\frac{5^7}{5^9}=7\cdot\frac{2^7}{5^2}=7\cdot\frac{128}{25}=\frac{896}{25}\)

a) \(\left(2x+1\right)^3\)

\(=\left(2x\right)^3+3.\left(2x\right)^2.1+3.2x.1+1\)

\(=8x^3+12x^2+6x+1\)

b) \(\left(x-3\right)^3\)

\(=x^3-3.x^2.3+3.x.3^2-3^3\)

\(=x^3-9x^2+27x-27\)

Bài 2: 

a: \(x^3+15x^2+75x+125=\left(x+5\right)^3\)

b: \(1-15y+75y^2-125y^3=\left(1-5y\right)^3\)

c: \(8x^3+4x^2y+\dfrac{3}{2}xy^2+8y^3=\left(2x+2y\right)^3\)

Bài 1:

\(\sqrt{17-12\sqrt{2}}=\sqrt{17-2\sqrt{72}}=\sqrt{8-2\sqrt{8.9}+9}=\sqrt{(\sqrt{8}-\sqrt{9})^2}\)

\(=|\sqrt{8}-\sqrt{9}|=3-2\sqrt{2}\)

\(\Rightarrow a=3; b=-\sqrt{2}\)

\(\Rightarrow a^2+b^2=9+2=11\)

Bài 1: 

Ta có: \(\sqrt{17-12\sqrt{2}}=a+b\sqrt{2}\)

\(\Leftrightarrow a+b\sqrt{2}=3-2\sqrt{2}\)

Suy ra: a=3; b=-2

\(\Leftrightarrow a^2+b^2=3^2+\left(-2\right)^2=9+4=13\)