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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{2}{5}}\right)^{\frac{2}{3}}\\= y^{ \frac{2}{5} . \frac{2}{3} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
2. \(\left(q^{\frac{-1}{2}}\right)^{\frac{1}{5}}\\= q^{ \frac{-1}{2} . \frac{1}{5} }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
3. \(\left(y^{\frac{2}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{2}{5} . \frac{1}{3} }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
4. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-2}{3} . (\frac{-1}{2}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
5. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-5}{3} . (\frac{-5}{4}) }= x^{\frac{25}{12}}\\=\sqrt[12]{ x^{25} }=|x^{2}|.\sqrt[12]{ x }\\---------------\)
6. \(\left(a^{\frac{2}{3}}\right)^{\frac{4}{3}}\\= a^{ \frac{2}{3} . \frac{4}{3} }= a^{\frac{8}{9}}\\=\sqrt[9]{ a^{8} }\\---------------\)
7. \(\left(y^{\frac{-1}{3}}\right)^{\frac{5}{2}}\\= y^{ \frac{-1}{3} . \frac{5}{2} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
8. \(\left(q^{-1}\right)^{-1}\\= q^{ -1 . (-1) }= q^{1}\\\\---------------\)
9. \(\left(x^{-1}\right)^{\frac{-2}{5}}\\= x^{ -1 . (\frac{-2}{5}) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
10. \(\left(a^{\frac{-3}{4}}\right)^{\frac{3}{2}}\\= a^{ \frac{-3}{4} . \frac{3}{2} }= a^{\frac{-9}{8}}\\=\frac{1}{\sqrt[8]{ a^{9} }}\\=\frac{1}{|a|.\sqrt[8]{ a }}=\frac{1}{|a|.\sqrt[8]{ a }} \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a^{2}|}\\---------------\)
11. \(\left(a^{1}\right)^{\frac{1}{2}}\\= a^{ 1 . \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(\left(x^{1}\right)^{\frac{5}{2}}\\= x^{ 1 . \frac{5}{2} }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)