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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{5}{4}}\right)^{\frac{1}{2}}\\= q^{ \frac{5}{4} . \frac{1}{2} }= q^{\frac{5}{8}}\\=\sqrt[8]{ q^{5} }\\---------------\)
2. \(\left(y^{\frac{1}{3}}\right)^{\frac{-2}{5}}\\= y^{ \frac{1}{3} . (\frac{-2}{5}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
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. \(\left(y^{\frac{-2}{3}}\right)^{-1}\\= y^{ \frac{-2}{3} . (-1) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
5. \(\left(x^{1}\right)^{\frac{1}{4}}\\= x^{ 1 . \frac{1}{4} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
6. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-3}{5} . (\frac{-5}{4}) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
7. \(\left(a^{\frac{-5}{6}}\right)^{-1}\\= a^{ \frac{-5}{6} . (-1) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
8. \(\left(x^{\frac{1}{3}}\right)^{-1}\\= x^{ \frac{1}{3} . (-1) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
9. \(\left(x^{\frac{-2}{5}}\right)^{\frac{-3}{4}}\\= x^{ \frac{-2}{5} . (\frac{-3}{4}) }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
10. \(\left(q^{\frac{4}{3}}\right)^{\frac{-1}{5}}\\= q^{ \frac{4}{3} . (\frac{-1}{5}) }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
11. \(\left(x^{-1}\right)^{\frac{-3}{4}}\\= x^{ -1 . (\frac{-3}{4}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
12. \(\left(q^{-1}\right)^{\frac{3}{5}}\\= q^{ -1 . \frac{3}{5} }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)