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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{1}{3} . (\frac{-1}{2}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
2. \(\left(x^{\frac{1}{3}}\right)^{1}\\= x^{ \frac{1}{3} . 1 }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-1}{3} . (\frac{-1}{3}) }= a^{\frac{1}{9}}\\=\sqrt[9]{ a }\\---------------\)
4. \(\left(y^{\frac{-1}{4}}\right)^{\frac{-3}{5}}\\= y^{ \frac{-1}{4} . (\frac{-3}{5}) }= y^{\frac{3}{20}}\\=\sqrt[20]{ y^{3} }\\---------------\)
5. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-1}{2} . (\frac{-3}{4}) }= q^{\frac{3}{8}}\\=\sqrt[8]{ q^{3} }\\---------------\)
6. \(\left(q^{\frac{-4}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{-4}{3} . \frac{1}{2} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
7. \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{3}}\\= a^{ \frac{1}{2} . (\frac{-1}{3}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
8. \(\left(q^{\frac{3}{5}}\right)^{-1}\\= q^{ \frac{3}{5} . (-1) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
9. \(\left(q^{\frac{1}{5}}\right)^{\frac{-4}{3}}\\= q^{ \frac{1}{5} . (\frac{-4}{3}) }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
10. \(\left(q^{1}\right)^{\frac{3}{5}}\\= q^{ 1 . \frac{3}{5} }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
11. \(\left(y^{\frac{2}{5}}\right)^{\frac{-5}{6}}\\= y^{ \frac{2}{5} . (\frac{-5}{6}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
12. \(\left(a^{\frac{2}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{2}{3} . \frac{1}{3} }= a^{\frac{2}{9}}\\=\sqrt[9]{ a^{2} }\\---------------\)