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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{3}{5}}\right)^{\frac{5}{6}}\\= x^{ \frac{3}{5} . \frac{5}{6} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
2. \(\left(a^{\frac{2}{3}}\right)^{\frac{-5}{6}}\\= a^{ \frac{2}{3} . (\frac{-5}{6}) }= a^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ a^{5} }}=\frac{1}{\sqrt[9]{ a^{5} }}. \color{purple}{\frac{\sqrt[9]{ a^{4} }}{\sqrt[9]{ a^{4} }}} \\=\frac{\sqrt[9]{ a^{4} }}{a}\\---------------\)
3. \(\left(q^{-1}\right)^{\frac{-4}{5}}\\= q^{ -1 . (\frac{-4}{5}) }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
4. \(\left(q^{\frac{1}{3}}\right)^{\frac{-2}{5}}\\= q^{ \frac{1}{3} . (\frac{-2}{5}) }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
5. \(\left(q^{\frac{5}{2}}\right)^{\frac{1}{4}}\\= q^{ \frac{5}{2} . \frac{1}{4} }= q^{\frac{5}{8}}\\=\sqrt[8]{ q^{5} }\\---------------\)
6. \(\left(x^{1}\right)^{1}\\= x^{ 1 . 1 }= x^{1}\\\\---------------\)
7. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-1}{2} . (\frac{-5}{2}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
8. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-2}{3} . (\frac{-2}{3}) }= x^{\frac{4}{9}}\\=\sqrt[9]{ x^{4} }\\---------------\)
9. \(\left(x^{\frac{5}{6}}\right)^{-2}\\= x^{ \frac{5}{6} . (-2) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
10. \(\left(x^{\frac{4}{5}}\right)^{1}\\= x^{ \frac{4}{5} . 1 }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
11. \(\left(a^{1}\right)^{\frac{-1}{4}}\\= a^{ 1 . (\frac{-1}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
12. \(\left(q^{\frac{1}{2}}\right)^{-1}\\= q^{ \frac{1}{2} . (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)