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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{2}}\right)^{\frac{2}{5}}\\= q^{ \frac{-1}{2} . \frac{2}{5} }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
2. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-1}{2} . (\frac{-2}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
3. \(\left(q^{\frac{1}{2}}\right)^{-1}\\= q^{ \frac{1}{2} . (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
4. \(\left(a^{\frac{-1}{6}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-1}{6} . (\frac{-1}{3}) }= a^{\frac{1}{18}}\\=\sqrt[18]{ a }\\---------------\)
5. \(\left(a^{\frac{-1}{5}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{5} . \frac{2}{3} }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
6. \(\left(q^{\frac{3}{2}}\right)^{\frac{-2}{3}}\\= q^{ \frac{3}{2} . (\frac{-2}{3}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
7. \(\left(y^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{1}{3} . \frac{1}{2} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
8. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-1}{3} . (\frac{-1}{3}) }= x^{\frac{1}{9}}\\=\sqrt[9]{ x }\\---------------\)
9. \(\left(q^{-1}\right)^{\frac{-1}{4}}\\= q^{ -1 . (\frac{-1}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
10. \(\left(y^{\frac{-1}{3}}\right)^{\frac{1}{3}}\\= y^{ \frac{-1}{3} . \frac{1}{3} }= y^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ y }}=\frac{1}{\sqrt[9]{ y }}. \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y}\\---------------\)
11. \(\left(x^{\frac{-2}{3}}\right)^{\frac{1}{5}}\\= x^{ \frac{-2}{3} . \frac{1}{5} }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
12. \(\left(y^{\frac{-2}{3}}\right)^{-1}\\= y^{ \frac{-2}{3} . (-1) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)