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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{5}}\right)^{\frac{5}{3}}\\= x^{ \frac{1}{5} . \frac{5}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
2. \(\left(q^{1}\right)^{-1}\\= q^{ 1 . (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
3. \(\left(y^{2}\right)^{-1}\\= y^{ 2 . (-1) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
4. \(\left(q^{\frac{1}{6}}\right)^{\frac{2}{3}}\\= q^{ \frac{1}{6} . \frac{2}{3} }= q^{\frac{1}{9}}\\=\sqrt[9]{ q }\\---------------\)
5. \(\left(a^{\frac{2}{5}}\right)^{1}\\= a^{ \frac{2}{5} . 1 }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
6. \(\left(q^{\frac{1}{5}}\right)^{\frac{-1}{6}}\\= q^{ \frac{1}{5} . (\frac{-1}{6}) }= q^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ q }}=\frac{1}{\sqrt[30]{ q }}. \color{purple}{\frac{\sqrt[30]{ q^{29} }}{\sqrt[30]{ q^{29} }}} \\=\frac{\sqrt[30]{ q^{29} }}{|q|}\\---------------\)
7. \(\left(y^{2}\right)^{\frac{-4}{5}}\\= y^{ 2 . (\frac{-4}{5}) }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)
8. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-3}{5}}\\= y^{ \frac{-1}{5} . (\frac{-3}{5}) }= y^{\frac{3}{25}}\\=\sqrt[25]{ y^{3} }\\---------------\)
9. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-5}{3} . (\frac{-5}{6}) }= x^{\frac{25}{18}}\\=\sqrt[18]{ x^{25} }=|x|.\sqrt[18]{ x^{7} }\\---------------\)
10. \(\left(a^{1}\right)^{2}\\= a^{ 1 . 2 }= a^{2}\\\\---------------\)
11. \(\left(y^{\frac{2}{5}}\right)^{\frac{-4}{5}}\\= y^{ \frac{2}{5} . (\frac{-4}{5}) }= y^{\frac{-8}{25}}\\=\frac{1}{\sqrt[25]{ y^{8} }}=\frac{1}{\sqrt[25]{ y^{8} }}. \color{purple}{\frac{\sqrt[25]{ y^{17} }}{\sqrt[25]{ y^{17} }}} \\=\frac{\sqrt[25]{ y^{17} }}{y}\\---------------\)
12. \(\left(x^{\frac{-1}{2}}\right)^{1}\\= x^{ \frac{-1}{2} . 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)