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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-4}{5}}\right)^{-1}\\= y^{ \frac{-4}{5} . (-1) }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
2. \(\left(x^{\frac{-4}{3}}\right)^{1}\\= x^{ \frac{-4}{3} . 1 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
3. \(\left(x^{\frac{-1}{2}}\right)^{-1}\\= x^{ \frac{-1}{2} . (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
4. \(\left(a^{\frac{1}{6}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{6} . \frac{1}{2} }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
5. \(\left(q^{\frac{-3}{4}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-3}{4} . (\frac{-1}{3}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
6. \(\left(y^{\frac{3}{2}}\right)^{-2}\\= y^{ \frac{3}{2} . (-2) }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
7. \(\left(q^{\frac{1}{6}}\right)^{\frac{-5}{6}}\\= q^{ \frac{1}{6} . (\frac{-5}{6}) }= q^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ q^{5} }}=\frac{1}{\sqrt[36]{ q^{5} }}. \color{purple}{\frac{\sqrt[36]{ q^{31} }}{\sqrt[36]{ q^{31} }}} \\=\frac{\sqrt[36]{ q^{31} }}{|q|}\\---------------\)
8. \(\left(q^{\frac{5}{6}}\right)^{\frac{1}{3}}\\= q^{ \frac{5}{6} . \frac{1}{3} }= q^{\frac{5}{18}}\\=\sqrt[18]{ q^{5} }\\---------------\)
9. \(\left(y^{\frac{5}{6}}\right)^{1}\\= y^{ \frac{5}{6} . 1 }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
10. \(\left(x^{\frac{-1}{2}}\right)^{\frac{5}{4}}\\= x^{ \frac{-1}{2} . \frac{5}{4} }= x^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ x^{5} }}=\frac{1}{\sqrt[8]{ x^{5} }}. \color{purple}{\frac{\sqrt[8]{ x^{3} }}{\sqrt[8]{ x^{3} }}} \\=\frac{\sqrt[8]{ x^{3} }}{|x|}\\---------------\)
11. \(\left(a^{\frac{5}{6}}\right)^{\frac{-1}{5}}\\= a^{ \frac{5}{6} . (\frac{-1}{5}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
12. \(\left(x^{\frac{-5}{3}}\right)^{\frac{1}{3}}\\= x^{ \frac{-5}{3} . \frac{1}{3} }= x^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ x^{5} }}=\frac{1}{\sqrt[9]{ x^{5} }}. \color{purple}{\frac{\sqrt[9]{ x^{4} }}{\sqrt[9]{ x^{4} }}} \\=\frac{\sqrt[9]{ x^{4} }}{x}\\---------------\)