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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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