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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{3}}\right)^{\frac{-3}{5}}\\= x^{ \frac{5}{3} . (\frac{-3}{5}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
2. \(\left(a^{\frac{1}{3}}\right)^{-2}\\= a^{ \frac{1}{3} . (-2) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
3. \(\left(q^{\frac{-5}{3}}\right)^{\frac{5}{6}}\\= q^{ \frac{-5}{3} . \frac{5}{6} }= q^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ q^{25} }}\\=\frac{1}{|q|.\sqrt[18]{ q^{7} }}=\frac{1}{|q|.\sqrt[18]{ q^{7} }} \color{purple}{\frac{\sqrt[18]{ q^{11} }}{\sqrt[18]{ q^{11} }}} \\=\frac{\sqrt[18]{ q^{11} }}{|q^{2}|}\\---------------\)
4. \(\left(y^{\frac{3}{5}}\right)^{-1}\\= y^{ \frac{3}{5} . (-1) }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
5. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-1}{3} . (\frac{-5}{2}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
6. \(\left(x^{1}\right)^{\frac{3}{5}}\\= x^{ 1 . \frac{3}{5} }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
7. \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{1}{3} . (\frac{-1}{3}) }= a^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ a }}=\frac{1}{\sqrt[9]{ a }}. \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a}\\---------------\)
8. \(\left(x^{\frac{-2}{5}}\right)^{-1}\\= x^{ \frac{-2}{5} . (-1) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
9. \(\left(q^{\frac{-3}{4}}\right)^{\frac{1}{3}}\\= q^{ \frac{-3}{4} . \frac{1}{3} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{\frac{3}{5}}\\= q^{ \frac{1}{2} . \frac{3}{5} }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
11. \(\left(q^{\frac{-1}{3}}\right)^{-1}\\= q^{ \frac{-1}{3} . (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
12. \(\left(y^{\frac{-5}{4}}\right)^{\frac{1}{2}}\\= y^{ \frac{-5}{4} . \frac{1}{2} }= y^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ y^{5} }}=\frac{1}{\sqrt[8]{ y^{5} }}. \color{purple}{\frac{\sqrt[8]{ y^{3} }}{\sqrt[8]{ y^{3} }}} \\=\frac{\sqrt[8]{ y^{3} }}{|y|}\\---------------\)