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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{-1}{3} . \frac{2}{3} }= y^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ y^{2} }}=\frac{1}{\sqrt[9]{ y^{2} }}. \color{purple}{\frac{\sqrt[9]{ y^{7} }}{\sqrt[9]{ y^{7} }}} \\=\frac{\sqrt[9]{ y^{7} }}{y}\\---------------\)
2. \(\left(a^{\frac{-5}{3}}\right)^{1}\\= a^{ \frac{-5}{3} . 1 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
3. \(\left(y^{\frac{-1}{6}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-1}{6} . (\frac{-5}{3}) }= y^{\frac{5}{18}}\\=\sqrt[18]{ y^{5} }\\---------------\)
4. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-1}{3} . (\frac{-5}{4}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
5. \(\left(q^{\frac{-1}{2}}\right)^{\frac{4}{5}}\\= q^{ \frac{-1}{2} . \frac{4}{5} }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
6. \(\left(y^{\frac{-5}{6}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-5}{6} . (\frac{-5}{6}) }= y^{\frac{25}{36}}\\=\sqrt[36]{ y^{25} }\\---------------\)
7. \(\left(y^{\frac{-1}{6}}\right)^{\frac{5}{3}}\\= y^{ \frac{-1}{6} . \frac{5}{3} }= y^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ y^{5} }}=\frac{1}{\sqrt[18]{ y^{5} }}. \color{purple}{\frac{\sqrt[18]{ y^{13} }}{\sqrt[18]{ y^{13} }}} \\=\frac{\sqrt[18]{ y^{13} }}{|y|}\\---------------\)
8. \(\left(x^{\frac{-4}{3}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-4}{3} . (\frac{-5}{6}) }= x^{\frac{10}{9}}\\=\sqrt[9]{ x^{10} }=x.\sqrt[9]{ x }\\---------------\)
9. \(\left(x^{1}\right)^{1}\\= x^{ 1 . 1 }= x^{1}\\\\---------------\)
10. \(\left(y^{\frac{5}{2}}\right)^{\frac{-5}{3}}\\= y^{ \frac{5}{2} . (\frac{-5}{3}) }= y^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ y^{25} }}\\=\frac{1}{|y^{4}|.\sqrt[6]{ y }}=\frac{1}{|y^{4}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{5}|}\\---------------\)
11. \(\left(x^{\frac{-1}{3}}\right)^{-1}\\= x^{ \frac{-1}{3} . (-1) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
12. \(\left(x^{\frac{-4}{5}}\right)^{-1}\\= x^{ \frac{-4}{5} . (-1) }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)