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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{\frac{-1}{4}}\\= q^{ 1 . (\frac{-1}{4}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
2. \(\left(q^{\frac{1}{5}}\right)^{\frac{-3}{5}}\\= q^{ \frac{1}{5} . (\frac{-3}{5}) }= q^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ q^{3} }}=\frac{1}{\sqrt[25]{ q^{3} }}. \color{purple}{\frac{\sqrt[25]{ q^{22} }}{\sqrt[25]{ q^{22} }}} \\=\frac{\sqrt[25]{ q^{22} }}{q}\\---------------\)
3. \(\left(x^{\frac{4}{3}}\right)^{\frac{1}{5}}\\= x^{ \frac{4}{3} . \frac{1}{5} }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
4. \(\left(q^{\frac{-3}{5}}\right)^{\frac{2}{5}}\\= q^{ \frac{-3}{5} . \frac{2}{5} }= q^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ q^{6} }}=\frac{1}{\sqrt[25]{ q^{6} }}. \color{purple}{\frac{\sqrt[25]{ q^{19} }}{\sqrt[25]{ q^{19} }}} \\=\frac{\sqrt[25]{ q^{19} }}{q}\\---------------\)
5. \(\left(x^{\frac{1}{6}}\right)^{\frac{1}{3}}\\= x^{ \frac{1}{6} . \frac{1}{3} }= x^{\frac{1}{18}}\\=\sqrt[18]{ x }\\---------------\)
6. \(\left(y^{1}\right)^{\frac{-1}{5}}\\= y^{ 1 . (\frac{-1}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
7. \(\left(a^{\frac{1}{5}}\right)^{\frac{-1}{5}}\\= a^{ \frac{1}{5} . (\frac{-1}{5}) }= a^{\frac{-1}{25}}\\=\frac{1}{\sqrt[25]{ a }}=\frac{1}{\sqrt[25]{ a }}. \color{purple}{\frac{\sqrt[25]{ a^{24} }}{\sqrt[25]{ a^{24} }}} \\=\frac{\sqrt[25]{ a^{24} }}{a}\\---------------\)
8. \(\left(y^{\frac{-5}{6}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-5}{6} . (\frac{-2}{3}) }= y^{\frac{5}{9}}\\=\sqrt[9]{ y^{5} }\\---------------\)
9. \(\left(x^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-1}{5} . (\frac{-1}{2}) }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
10. \(\left(y^{\frac{3}{5}}\right)^{\frac{-5}{3}}\\= y^{ \frac{3}{5} . (\frac{-5}{3}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
11. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-4}{5}}\\= q^{ \frac{-3}{5} . (\frac{-4}{5}) }= q^{\frac{12}{25}}\\=\sqrt[25]{ q^{12} }\\---------------\)
12. \(\left(y^{1}\right)^{\frac{3}{4}}\\= y^{ 1 . \frac{3}{4} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)