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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{-1}\right)^{\frac{3}{5}}\\= x^{ -1 . \frac{3}{5} }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
2. \(\left(y^{\frac{-3}{5}}\right)^{\frac{1}{4}}\\= y^{ \frac{-3}{5} . \frac{1}{4} }= y^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ y^{3} }}=\frac{1}{\sqrt[20]{ y^{3} }}. \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y|}\\---------------\)
3. \(\left(y^{-1}\right)^{\frac{4}{3}}\\= y^{ -1 . \frac{4}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
4. \(\left(a^{1}\right)^{\frac{-1}{5}}\\= a^{ 1 . (\frac{-1}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
5. \(\left(a^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{-1}{2} . \frac{1}{2} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
6. \(\left(a^{\frac{-5}{3}}\right)^{-1}\\= a^{ \frac{-5}{3} . (-1) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
7. \(\left(q^{\frac{5}{3}}\right)^{\frac{-5}{4}}\\= q^{ \frac{5}{3} . (\frac{-5}{4}) }= q^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ q^{25} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q }}=\frac{1}{|q^{2}|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{3}|}\\---------------\)
8. \(\left(a^{\frac{1}{2}}\right)^{-1}\\= a^{ \frac{1}{2} . (-1) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
9. \(\left(a^{-1}\right)^{\frac{-1}{5}}\\= a^{ -1 . (\frac{-1}{5}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
10. \(\left(q^{\frac{-3}{4}}\right)^{\frac{2}{3}}\\= q^{ \frac{-3}{4} . \frac{2}{3} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
11. \(\left(x^{\frac{-3}{2}}\right)^{\frac{5}{2}}\\= x^{ \frac{-3}{2} . \frac{5}{2} }= x^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ x^{15} }}\\=\frac{1}{|x^{3}|.\sqrt[4]{ x^{3} }}=\frac{1}{|x^{3}|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{4}|}\\---------------\)
12. \(\left(q^{\frac{-5}{2}}\right)^{-1}\\= q^{ \frac{-5}{2} . (-1) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)