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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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