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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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