Verified answer

1.

[tex](-2x^5)^4\cdot\left(-\dfrac{1}{32}xy^2\right)=32x^{20}\cdot\left(-\dfrac{1}{32}xy^2\right)=-x^{21}y^2[/tex]

2.

[tex]4x^2+3x\cdot x^2-5x\cdot x+x^3-5=4x^2+3x^3-5x^2+x^3-5=4x^3-x^2-5[/tex]

3.

[tex](2x^2-3x+5)+(5x-x^2-3)=2x^2-3x+5+5x-x^2-3=x^2+2x+2\\(2x^2-3x+5)-(5x-x^2-3)=2x^2-3x+5-5x+x^2+3=3x^2-8x+8[/tex]

4.

а) [tex]16a^3-2a^2(8a-3)=16a^3-16a^3+6a^2=6a^2[/tex]

б) [tex](a-2)(a-3)-a(a-5)=a^2-5a+6-a^2+5a=6[/tex]

5.

a) [tex]-25y^2-10x^2y=-5y(5y+2x^2)[/tex]

б) [tex]8x^5b^2-12x^3b^3+4x^4=4x^3(2x^2b^2-3b^3+x)[/tex]

в) [tex]3a+ab^2-a^2b-3b=3(a-b)+ab(b-a)=(3-ab)(a-b)[/tex]

6.

[tex]\dfrac{a^2\cdot(a^3)^4}{(a^4)^3}=\dfrac{a^2\cdot a^{3\cdot4}}{a^{4\cdot3}}=a^2\\\left(-1\dfrac{1}{3}\right)^2=\left(-\dfrac{4}{3}\right)^2=\dfrac{16}{9}[/tex]

7.

[tex]\left(\dfrac{3}{5}x^{-3}y^4\right)^{-2}\cdot15x^3y=\dfrac{25}{9}x^{-3\cdot(-2)}y^{4\cdot(-2)}\cdot15x^3y=\dfrac{125}{3}x^6y^{-8}\cdot x^3y=\dfrac{125}{3}x^9y^{-7}[/tex]