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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{5}}\right)^{\frac{3}{4}}\\= a^{ \frac{-1}{5} . \frac{3}{4} }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
2. \(\left(a^{-1}\right)^{\frac{-5}{6}}\\= a^{ -1 . (\frac{-5}{6}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
3. \(\left(y^{\frac{5}{2}}\right)^{\frac{-1}{4}}\\= y^{ \frac{5}{2} . (\frac{-1}{4}) }= y^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ y^{5} }}=\frac{1}{\sqrt[8]{ y^{5} }}. \color{purple}{\frac{\sqrt[8]{ y^{3} }}{\sqrt[8]{ y^{3} }}} \\=\frac{\sqrt[8]{ y^{3} }}{|y|}\\---------------\)
4. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-1}{2} . (\frac{-1}{4}) }= q^{\frac{1}{8}}\\=\sqrt[8]{ q }\\---------------\)
5. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-1}{2} . (\frac{-4}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
6. \(\left(a^{\frac{2}{3}}\right)^{\frac{-5}{6}}\\= a^{ \frac{2}{3} . (\frac{-5}{6}) }= a^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ a^{5} }}=\frac{1}{\sqrt[9]{ a^{5} }}. \color{purple}{\frac{\sqrt[9]{ a^{4} }}{\sqrt[9]{ a^{4} }}} \\=\frac{\sqrt[9]{ a^{4} }}{a}\\---------------\)
7. \(\left(q^{\frac{-1}{6}}\right)^{1}\\= q^{ \frac{-1}{6} . 1 }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
8. \(\left(y^{\frac{1}{2}}\right)^{1}\\= y^{ \frac{1}{2} . 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
9. \(\left(q^{1}\right)^{\frac{-3}{4}}\\= q^{ 1 . (\frac{-3}{4}) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
10. \(\left(a^{\frac{1}{3}}\right)^{\frac{-5}{6}}\\= a^{ \frac{1}{3} . (\frac{-5}{6}) }= a^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ a^{5} }}=\frac{1}{\sqrt[18]{ a^{5} }}. \color{purple}{\frac{\sqrt[18]{ a^{13} }}{\sqrt[18]{ a^{13} }}} \\=\frac{\sqrt[18]{ a^{13} }}{|a|}\\---------------\)
11. \(\left(y^{\frac{-1}{4}}\right)^{\frac{2}{3}}\\= y^{ \frac{-1}{4} . \frac{2}{3} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
12. \(\left(x^{\frac{-5}{2}}\right)^{\frac{2}{3}}\\= x^{ \frac{-5}{2} . \frac{2}{3} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)