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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-1}{3} . (\frac{-5}{3}) }= y^{\frac{5}{9}}\\=\sqrt[9]{ y^{5} }\\---------------\)
2. \(\left(q^{\frac{-3}{4}}\right)^{\frac{5}{4}}\\= q^{ \frac{-3}{4} . \frac{5}{4} }= q^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ q^{15} }}=\frac{1}{\sqrt[16]{ q^{15} }}. \color{purple}{\frac{\sqrt[16]{ q }}{\sqrt[16]{ q }}} \\=\frac{\sqrt[16]{ q }}{|q|}\\---------------\)
3. \(\left(x^{1}\right)^{\frac{2}{5}}\\= x^{ 1 . \frac{2}{5} }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
4. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{3} . \frac{1}{2} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
5. \(\left(a^{2}\right)^{\frac{1}{3}}\\= a^{ 2 . \frac{1}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
6. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-1}{4} . (\frac{-1}{3}) }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
7. \(\left(y^{\frac{1}{5}}\right)^{\frac{-1}{4}}\\= y^{ \frac{1}{5} . (\frac{-1}{4}) }= y^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ y }}=\frac{1}{\sqrt[20]{ y }}. \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y|}\\---------------\)
8. \(\left(q^{\frac{1}{2}}\right)^{\frac{5}{3}}\\= q^{ \frac{1}{2} . \frac{5}{3} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
9. \(\left(x^{\frac{2}{3}}\right)^{\frac{2}{5}}\\= x^{ \frac{2}{3} . \frac{2}{5} }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
10. \(\left(a^{\frac{2}{5}}\right)^{1}\\= a^{ \frac{2}{5} . 1 }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
11. \(\left(y^{\frac{-1}{5}}\right)^{\frac{4}{3}}\\= y^{ \frac{-1}{5} . \frac{4}{3} }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
12. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-1}{2} . (\frac{-3}{2}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)