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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-5}{4}}\right)^{-1}\\= q^{ \frac{-5}{4} . (-1) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
2. \(\left(y^{\frac{-5}{6}}\right)^{1}\\= y^{ \frac{-5}{6} . 1 }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
3. \(\left(q^{-1}\right)^{\frac{1}{4}}\\= q^{ -1 . \frac{1}{4} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
4. \(\left(q^{1}\right)^{\frac{1}{4}}\\= q^{ 1 . \frac{1}{4} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
5. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-2}{3} . (\frac{-1}{3}) }= y^{\frac{2}{9}}\\=\sqrt[9]{ y^{2} }\\---------------\)
6. \(\left(a^{\frac{-1}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{3} . \frac{2}{3} }= a^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ a^{2} }}=\frac{1}{\sqrt[9]{ a^{2} }}. \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a}\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{-5}{3}}\\= a^{ -1 . (\frac{-5}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
8. \(\left(a^{\frac{-1}{2}}\right)^{\frac{3}{5}}\\= a^{ \frac{-1}{2} . \frac{3}{5} }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
9. \(\left(y^{\frac{1}{3}}\right)^{\frac{1}{6}}\\= y^{ \frac{1}{3} . \frac{1}{6} }= y^{\frac{1}{18}}\\=\sqrt[18]{ y }\\---------------\)
10. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-2}{5}}\\= a^{ \frac{-5}{3} . (\frac{-2}{5}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
11. \(\left(q^{\frac{-1}{5}}\right)^{1}\\= q^{ \frac{-1}{5} . 1 }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
12. \(\left(a^{\frac{1}{6}}\right)^{\frac{5}{6}}\\= a^{ \frac{1}{6} . \frac{5}{6} }= a^{\frac{5}{36}}\\=\sqrt[36]{ a^{5} }\\---------------\)