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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{4}{3}}\right)^{\frac{1}{3}}\\= y^{ \frac{4}{3} . \frac{1}{3} }= y^{\frac{4}{9}}\\=\sqrt[9]{ y^{4} }\\---------------\)
2. \(\left(y^{\frac{-1}{6}}\right)^{\frac{-1}{6}}\\= y^{ \frac{-1}{6} . (\frac{-1}{6}) }= y^{\frac{1}{36}}\\=\sqrt[36]{ y }\\---------------\)
3. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-1}{4} . (\frac{-1}{3}) }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
4. \(\left(a^{\frac{-1}{4}}\right)^{\frac{5}{2}}\\= a^{ \frac{-1}{4} . \frac{5}{2} }= a^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ a^{5} }}=\frac{1}{\sqrt[8]{ a^{5} }}. \color{purple}{\frac{\sqrt[8]{ a^{3} }}{\sqrt[8]{ a^{3} }}} \\=\frac{\sqrt[8]{ a^{3} }}{|a|}\\---------------\)
5. \(\left(x^{1}\right)^{\frac{2}{3}}\\= x^{ 1 . \frac{2}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
6. \(\left(a^{\frac{2}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{2}{3} . \frac{2}{3} }= a^{\frac{4}{9}}\\=\sqrt[9]{ a^{4} }\\---------------\)
7. \(\left(x^{\frac{-1}{4}}\right)^{\frac{3}{5}}\\= x^{ \frac{-1}{4} . \frac{3}{5} }= x^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ x^{3} }}=\frac{1}{\sqrt[20]{ x^{3} }}. \color{purple}{\frac{\sqrt[20]{ x^{17} }}{\sqrt[20]{ x^{17} }}} \\=\frac{\sqrt[20]{ x^{17} }}{|x|}\\---------------\)
8. \(\left(q^{\frac{4}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{4}{5} . \frac{1}{3} }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
9. \(\left(q^{\frac{-3}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{-3}{2} . \frac{1}{2} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
10. \(\left(x^{\frac{-5}{2}}\right)^{\frac{1}{3}}\\= x^{ \frac{-5}{2} . \frac{1}{3} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
11. \(\left(y^{\frac{1}{2}}\right)^{\frac{-4}{5}}\\= y^{ \frac{1}{2} . (\frac{-4}{5}) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
12. \(\left(y^{\frac{-3}{4}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-3}{4} . (\frac{-5}{4}) }= y^{\frac{15}{16}}\\=\sqrt[16]{ y^{15} }\\---------------\)