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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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