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Werk uit m.b.v. de rekenregels

1. \(\left(y^{\frac{4}{5}}\right)^{\frac{3}{4}}\)
2. \(\left(x^{1}\right)^{\frac{3}{4}}\)
3. \(\left(a^{\frac{-3}{5}}\right)^{\frac{1}{5}}\)
4. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{2}}\)
5. \(\left(a^{\frac{3}{2}}\right)^{\frac{-5}{6}}\)
6. \(\left(a^{\frac{-1}{2}}\right)^{\frac{4}{3}}\)
7. \(\left(x^{\frac{2}{5}}\right)^{-1}\)
8. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-1}{6}}\)
9. \(\left(y^{\frac{-4}{3}}\right)^{\frac{1}{6}}\)
10. \(\left(a^{\frac{-5}{2}}\right)^{\frac{5}{3}}\)
11. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-5}{2}}\)
12. \(\left(a^{\frac{5}{2}}\right)^{\frac{5}{2}}\)

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{4}{5}}\right)^{\frac{3}{4}}\\= y^{ \frac{4}{5} . \frac{3}{4} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
2. \(\left(x^{1}\right)^{\frac{3}{4}}\\= x^{ 1 . \frac{3}{4} }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
3. \(\left(a^{\frac{-3}{5}}\right)^{\frac{1}{5}}\\= a^{ \frac{-3}{5} . \frac{1}{5} }= a^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ a^{3} }}=\frac{1}{\sqrt[25]{ a^{3} }}. \color{purple}{\frac{\sqrt[25]{ a^{22} }}{\sqrt[25]{ a^{22} }}} \\=\frac{\sqrt[25]{ a^{22} }}{a}\\---------------\)
4. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{1}{2} . \frac{1}{2} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
5. \(\left(a^{\frac{3}{2}}\right)^{\frac{-5}{6}}\\= a^{ \frac{3}{2} . (\frac{-5}{6}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
6. \(\left(a^{\frac{-1}{2}}\right)^{\frac{4}{3}}\\= a^{ \frac{-1}{2} . \frac{4}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
7. \(\left(x^{\frac{2}{5}}\right)^{-1}\\= x^{ \frac{2}{5} . (-1) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
8. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-4}{5} . (\frac{-1}{6}) }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
9. \(\left(y^{\frac{-4}{3}}\right)^{\frac{1}{6}}\\= y^{ \frac{-4}{3} . \frac{1}{6} }= y^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ y^{2} }}=\frac{1}{\sqrt[9]{ y^{2} }}. \color{purple}{\frac{\sqrt[9]{ y^{7} }}{\sqrt[9]{ y^{7} }}} \\=\frac{\sqrt[9]{ y^{7} }}{y}\\---------------\)
10. \(\left(a^{\frac{-5}{2}}\right)^{\frac{5}{3}}\\= a^{ \frac{-5}{2} . \frac{5}{3} }= a^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ a^{25} }}\\=\frac{1}{|a^{4}|.\sqrt[6]{ a }}=\frac{1}{|a^{4}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{5}|}\\---------------\)
11. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-5}{2}}\\= x^{ \frac{-1}{3} . (\frac{-5}{2}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
12. \(\left(a^{\frac{5}{2}}\right)^{\frac{5}{2}}\\= a^{ \frac{5}{2} . \frac{5}{2} }= a^{\frac{25}{4}}\\=\sqrt[4]{ a^{25} }=|a^{6}|.\sqrt[4]{ a }\\---------------\)