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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{3}}\right)^{-1}\\= y^{ \frac{1}{3} . (-1) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
2. \(\left(a^{\frac{-5}{4}}\right)^{-1}\\= a^{ \frac{-5}{4} . (-1) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
3. \(\left(a^{\frac{2}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{2}{3} . \frac{1}{2} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
4. \(\left(y^{\frac{1}{3}}\right)^{\frac{-2}{5}}\\= y^{ \frac{1}{3} . (\frac{-2}{5}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
5. \(\left(a^{\frac{-5}{4}}\right)^{1}\\= a^{ \frac{-5}{4} . 1 }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
6. \(\left(q^{-1}\right)^{\frac{-5}{4}}\\= q^{ -1 . (\frac{-5}{4}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
7. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-4}{3}}\\= x^{ \frac{-1}{2} . (\frac{-4}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
8. \(\left(q^{\frac{1}{5}}\right)^{\frac{2}{3}}\\= q^{ \frac{1}{5} . \frac{2}{3} }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
9. \(\left(a^{\frac{2}{3}}\right)^{\frac{-1}{6}}\\= a^{ \frac{2}{3} . (\frac{-1}{6}) }= a^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ a }}=\frac{1}{\sqrt[9]{ a }}. \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a}\\---------------\)
10. \(\left(a^{\frac{-4}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{-4}{3} . \frac{1}{2} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
11. \(\left(y^{-1}\right)^{-2}\\= y^{ -1 . (-2) }= y^{2}\\\\---------------\)
12. \(\left(q^{1}\right)^{\frac{3}{5}}\\= q^{ 1 . \frac{3}{5} }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)