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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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