Bài 1

12³.3²

=(2.6)³.3²

=2³.6³.3²

=2³.2³.3⁵

=2³⁺³.3⁵

=2⁶.3⁵

Bài 2:Tìm X

(x-2)⁵=243

(x-2)⁵=3⁵

=>(x-2)=3

     x    =3+2

     x    =5

    2^x+2^x+4=272

    2^x+2^x+4=2⁴+2⁸

=>     x     =4

=12.12.12.3.3=3.4.3.4.3.4.3.3=3.3.3.3.3.4.4.4=3 mũ 5 . 4 mũ 3

\(P\left(x\right)=3x^2+7+2x^4-3x^2-4-5x+2x^3\)

\(=2x^4+2x^3+\left(3x^2-3x^2\right)-5x-4+7\)

\(=2x^4+2x^3-5x+3\)

\(Q\left(x\right)=-3x^3+2x^2-x^4+x+x^3+4x-2+5x^4\)

\(=\left(5x^4-x^4\right)+\left(-3x^3+x^3\right)+2x^2+\left(x+4x\right)-2\)

\(=4x^4-2x^3+2x^2+5x-2\)

\(13^4\times16^2=13\times13\times13\times13\times16\times16\)

\(=\left(13\times13\right)\times\left(13\times13\right)\times\left(13\times6\right)\)

\(=28561\times256\)

\(=7311616=52^4\)

   13⁴.16² 

= 13⁴.(4²)²

= 13⁴.4⁴

= (13.4)⁴

= 52⁴

2⁵ . 4³ = 2⁵ . (2²)³ = 2⁵ . 2⁶ = 2^{5 + 6} = 2¹¹

\(2^{11}\)

\(2^5\cdot4^3=2^5\cdot2^6=2^{11}\)

\(4^2\times8^2\)

\(=\left(2^2\right)^2\times\left(2^3\right)^2\)

\(=2^4\times2^6=2^{10}\)

4²x8²=(4x8)²

         =32²

a) \(x^{16}=x^{10}\cdot x^6\)

b) \(x^{16}=\left(x^4\right)^4\)

c) \(x^{16}=x^{20}\div x^4\)

a) \(\dfrac{9}{4}-3y+y^2\)

\(=\left(\dfrac{3}{2}\right)^2-3y+y^2\)

\(=y^2-2\cdot\dfrac{3}{2}\cdot y+\left(\dfrac{3}{2}\right)^2\)

\(=\left(y-\dfrac{3}{2}\right)^2\)

b) \(x^3+6x^2y+12xy^2+8y^3\)

\(=x^3+6x^2y+12xy^2+\left(2y\right)^3\)

\(=x^3+3\cdot x^2\cdot2y+3\cdot x\cdot\left(2y\right)^2+\left(2y\right)^3\)

\(=\left(x+2y\right)^2\)