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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-2}\right)^{\frac{1}{6}}\\= q^{ -2 . \frac{1}{6} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
2. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-1}{2} . (\frac{-3}{4}) }= q^{\frac{3}{8}}\\=\sqrt[8]{ q^{3} }\\---------------\)
3. \(\left(a^{\frac{1}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{5} . (\frac{-1}{2}) }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
4. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-1}{3} . (\frac{-2}{3}) }= a^{\frac{2}{9}}\\=\sqrt[9]{ a^{2} }\\---------------\)
5. \(\left(a^{1}\right)^{\frac{-4}{5}}\\= a^{ 1 . (\frac{-4}{5}) }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
6. \(\left(y^{\frac{-2}{5}}\right)^{1}\\= y^{ \frac{-2}{5} . 1 }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
7. \(\left(y^{\frac{5}{4}}\right)^{\frac{5}{4}}\\= y^{ \frac{5}{4} . \frac{5}{4} }= y^{\frac{25}{16}}\\=\sqrt[16]{ y^{25} }=|y|.\sqrt[16]{ y^{9} }\\---------------\)
8. \(\left(q^{\frac{1}{2}}\right)^{-1}\\= q^{ \frac{1}{2} . (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
9. \(\left(a^{\frac{-1}{4}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{4} . (\frac{-1}{2}) }= a^{\frac{1}{8}}\\=\sqrt[8]{ a }\\---------------\)
10. \(\left(q^{\frac{-5}{4}}\right)^{\frac{-5}{6}}\\= q^{ \frac{-5}{4} . (\frac{-5}{6}) }= q^{\frac{25}{24}}\\=\sqrt[24]{ q^{25} }=|q|.\sqrt[24]{ q }\\---------------\)
11. \(\left(y^{\frac{-2}{5}}\right)^{-1}\\= y^{ \frac{-2}{5} . (-1) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
12. \(\left(a^{1}\right)^{\frac{-1}{3}}\\= a^{ 1 . (\frac{-1}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)