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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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