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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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