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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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