Simplify:
(x20y−10z55)÷x3y3(\sqrt[5]{x^{20}y^{-10}z^5}) ÷ \dfrac{x^3}{y^3}(5x20y−10z5)÷y3x3
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(x20y−10z55)÷x3y3=(x205y−105z55)÷x3y3=(x4y−2z1)÷x3y3=(x4y−2z1)×y3x3=(x4−3y−2+3z)=(x1y1z)=xyz(\sqrt[5]{x^{20}y^{-10}z^5}) ÷ \dfrac{x^3}{y^3}\\[1em] = (x^{\dfrac{20}{5}}y^{\dfrac{-10}{5}}z^{\dfrac{5}{5}}) ÷ \dfrac{x^3}{y^3}\\[1em] = (x^4y^{-2}z^1) ÷ \dfrac{x^3}{y^3}\\[1em] = (x^4y^{-2}z^1) \times \dfrac{y^3}{x^3}\\[1em] = (x^{4-3}y^{-2+3}z)\\[1em] = (x^1y^1z)\\[1em] = xyz(5x20y−10z5)÷y3x3=(x520y5−10z55)÷y3x3=(x4y−2z1)÷y3x3=(x4y−2z1)×x3y3=(x4−3y−2+3z)=(x1y1z)=xyz
(x20y−10z55)÷x3y3=xyz(\sqrt[5]{x^{20}y^{-10}z^5}) ÷ \dfrac{x^3}{y^3} = xyz(5x20y−10z5)÷y3x3=xyz
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(−2x23y−32)6(-2x^{\dfrac{2}{3}}y^{\dfrac{-3}{2}})^6(−2x32y2−3)6
Simplify: (xa+b)a−b.(xb+c)b−c.(xc+a)c−a(x^{a+b})^{a-b}.(x^{b+c})^{b-c}.(x^{c+a})^{c-a}(xa+b)a−b.(xb+c)b−c.(xc+a)c−a
[256a1681b4]−34\Big[\dfrac{256a^{16}}{81b^4}\Big]^{\dfrac{-3}{4}}[81b4256a16]4−3
Simplify and express as positive indices:
(a−2b)−2.(ab)−3(a^{-2}b)^{-2}.(ab)^{-3}(a−2b)−2.(ab)−3
