+521 \(\sqrt[3]{{96u^4 \over 14w^7}}* \sqrt[4]{{28u^3w \over 3}}\)
+301 \(\sqrt[3]{\frac{96u^4}{14w^7}}*\sqrt[4]{\frac{28u^3w}{3}}\\ =\\ (\frac{96u^4}{14w^7})^\frac{1}{3}*(\frac{28u^3w}{3})^\frac{1}{4}\\ =\\ \frac{96^\frac{1}{3}u^\frac{4}{3}}{14^\frac{1}{3}w^\frac{7}{3}}*\frac{28^\frac{1}{4}u^\frac{3}{4}w^\frac{1}{4}}{3^\frac{1}{4}}\\ =\\ \frac{4^\frac{1}{3}*14^\frac{1}{3}u^\frac{4}{3}}{14^\frac{1}{3}w^\frac{7}{3}}*\frac{28^\frac{1}{4}u^\frac{3}{4}w^\frac{1}{4}}{3^\frac{1}{4}}\\\)
\(=\\ \frac{4^\frac{1}{3}u^\frac{4}{3}}{w^\frac{7}{3}}*\frac{28^\frac{1}{4}u^\frac{3}{4}w^\frac{1}{4}}{3^\frac{1}{4}}\\ =\\ 4^\frac{1}{3}u^\frac{4}{3}w^{-\frac{7}{3}}*28^\frac{1}{4}u^\frac{3}{4}w^\frac{1}{4}3^{-\frac{1}{4}}\\ =\\ 4^\frac{1}{3}u^\frac{16}{12}w^{-\frac{28}{12}}*28^\frac{1}{4}u^\frac{9}{12}w^\frac{3}{12}3^{-\frac{1}{4}}\\ =\\ 4^\frac{4}{12}u^\frac{25}{12}w^{-\frac{25}{12}}*28^\frac{3}{12}3^{-\frac{3}{12}}\\ =\\ \sqrt[12]{4^4u^{25}w^{-25}*28^33^{-3}}\)
=
\(\sqrt[12]{\frac{4^4u^{25}}{w^{25}}*\frac{28^3}{3^{3}}}\\ =\\ \sqrt[12]{\frac{256u^{25}}{w^{25}}*\frac{21952}{27}}\\ =\\ \sqrt[12]{\frac{5619712u^{25}}{27w^{25}}}\\\)
Also ich bin mir wirklich nicht sicher, ob das richtig ist. Aber mehr ist mir dazu nicht eingefallen.
+14993 Schreibe alles unter einer Wurzel
\(\sqrt[3]{{96u^4 \over 14w^7}}* \sqrt[4]{{28u^3w \over 3}}\)
Ich rechne mal nach.
\(\sqrt[3]{{96u^4 \over 14w^7}}* \sqrt[4]{{28u^3w \over 3}}\\ =(2^5\cdot 3)^{1/3}\cdot (2\cdot 7)^{-1/3}\cdot (2^2\cdot 7)^{1/4}\cdot 3^{-1/4}\\ \cdot u^{4/3}\cdot w^{-7/3}\cdot u^{3/4}\cdot w^{1/4}\)
\(=(\frac{2^5\cdot 3}{2\cdot 7})^{1/3}\cdot (\frac{2^2\cdot 7}{3})^{1/4}\cdot (\frac{u^4}{w^7})^{1/3}\cdot (\frac{u^3\cdot w}{1})^{1/4}\)
\(=\sqrt[3]{\frac{2^4\cdot 3\cdot u^4}{7\cdot w^7}}\cdot \sqrt[4]{\frac{2^2\cdot 7\cdot u^3\cdot w}{3}}\)
\(\color{blue}a^{n/3}\cdot b^{m/4} =a^{4n/12}\cdot b^{3m/12}\)
\(\large =\sqrt[12]{\frac{2^{16}\cdot 3^4\cdot u^{16}}{7^4\cdot w^{28}}}\cdot \sqrt[12]{\frac{2^6\cdot 7^3\cdot u^9\cdot w^3}{3^3}}\\ \large \color{blue}=\sqrt[12]{\frac{2^{22 }\cdot 3\cdot u^{25}}{7\cdot w^{25}}}\\ \large =\frac{2\cdot u}{w^2}\cdot \sqrt[12]{\frac{2^{10}\cdot 3\cdot u^{13}}{7\cdot w}}\)
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