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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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