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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-2}{3}}\right)^{-1}\\= q^{ \frac{-2}{3} . (-1) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
2. \(\left(a^{\frac{5}{3}}\right)^{\frac{-5}{6}}\\= a^{ \frac{5}{3} . (\frac{-5}{6}) }= a^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ a^{25} }}\\=\frac{1}{|a|.\sqrt[18]{ a^{7} }}=\frac{1}{|a|.\sqrt[18]{ a^{7} }} \color{purple}{\frac{\sqrt[18]{ a^{11} }}{\sqrt[18]{ a^{11} }}} \\=\frac{\sqrt[18]{ a^{11} }}{|a^{2}|}\\---------------\)
3. \(\left(x^{\frac{-2}{5}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-2}{5} . (\frac{-3}{2}) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
4. \(\left(y^{\frac{-5}{3}}\right)^{\frac{1}{3}}\\= y^{ \frac{-5}{3} . \frac{1}{3} }= y^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ y^{5} }}=\frac{1}{\sqrt[9]{ y^{5} }}. \color{purple}{\frac{\sqrt[9]{ y^{4} }}{\sqrt[9]{ y^{4} }}} \\=\frac{\sqrt[9]{ y^{4} }}{y}\\---------------\)
5. \(\left(a^{\frac{5}{6}}\right)^{\frac{-5}{6}}\\= a^{ \frac{5}{6} . (\frac{-5}{6}) }= a^{\frac{-25}{36}}\\=\frac{1}{\sqrt[36]{ a^{25} }}=\frac{1}{\sqrt[36]{ a^{25} }}. \color{purple}{\frac{\sqrt[36]{ a^{11} }}{\sqrt[36]{ a^{11} }}} \\=\frac{\sqrt[36]{ a^{11} }}{|a|}\\---------------\)
6. \(\left(x^{\frac{1}{2}}\right)^{\frac{2}{5}}\\= x^{ \frac{1}{2} . \frac{2}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
7. \(\left(q^{\frac{-1}{3}}\right)^{-1}\\= q^{ \frac{-1}{3} . (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
8. \(\left(y^{\frac{1}{2}}\right)^{\frac{-2}{5}}\\= y^{ \frac{1}{2} . (\frac{-2}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
9. \(\left(y^{\frac{5}{3}}\right)^{\frac{-3}{2}}\\= y^{ \frac{5}{3} . (\frac{-3}{2}) }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
10. \(\left(a^{\frac{3}{2}}\right)^{\frac{1}{4}}\\= a^{ \frac{3}{2} . \frac{1}{4} }= a^{\frac{3}{8}}\\=\sqrt[8]{ a^{3} }\\---------------\)
11. \(\left(x^{\frac{5}{6}}\right)^{-1}\\= x^{ \frac{5}{6} . (-1) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
12. \(\left(q^{-1}\right)^{\frac{3}{4}}\\= q^{ -1 . \frac{3}{4} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)