Simplify:
[256a1681b4]−34\Big[\dfrac{256a^{16}}{81b^4}\Big]^{\dfrac{-3}{4}}[81b4256a16]4−3
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[256a1681b4]−34=[28a1634b4]−34=[22a43b]4×−34=[22a43b]−3=[3b22a4]3=[33b326a12]=[27b364a12]=[2764]a−12b3\Big[\dfrac{256a^{16}}{81b^4}\Big]^{\dfrac{-3}{4}}\\[1em] = \Big[\dfrac{2^{8}a^{16}}{3^4b^4}\Big]^{\dfrac{-3}{4}}\\[1em] = \Big[\dfrac{2^{2}a^{4}}{3b}\Big]^{4\times\dfrac{-3}{4}}\\[1em] = \Big[\dfrac{2^{2}a^{4}}{3b}\Big]^{-3}\\[1em] = \Big[\dfrac{3b}{2^{2}a^{4}}\Big]^{3}\\[1em] = \Big[\dfrac{3^3b^3}{2^{6}a^{12}}\Big]\\[1em] = \Big[\dfrac{27b^3}{64a^{12}}\Big]\\[1em] = \Big[\dfrac{27}{64}\Big]a^{-12}b^3[81b4256a16]4−3=[34b428a16]4−3=[3b22a4]4×4−3=[3b22a4]−3=[22a43b]3=[26a1233b3]=[64a1227b3]=[6427]a−12b3
[256a1681b4]−34=[2764]a−12b3\Big[\dfrac{256a^{16}}{81b^4}\Big]^{\dfrac{-3}{4}} = \Big[\dfrac{27}{64}\Big]a^{-12}b^3[81b4256a16]4−3=[6427]a−12b3
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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
(x20y−10z55)÷x3y3(\sqrt[5]{x^{20}y^{-10}z^5}) ÷ \dfrac{x^3}{y^3}(5x20y−10z5)÷y3x3
Simplify and express as positive indices:
(a−2b)−2.(ab)−3(a^{-2}b)^{-2}.(ab)^{-3}(a−2b)−2.(ab)−3
(xny−m)4×(x3y−2)−n(x^ny^{-m})^4\times(x^3y^{-2})^{-n}(xny−m)4×(x3y−2)−n
