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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-3}{5}}\right)^{2}\\= a^{ \frac{-3}{5} . 2 }= a^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ a^{6} }}\\=\frac{1}{a.\sqrt[5]{ a }}=\frac{1}{a.\sqrt[5]{ a }} \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a^{2}}\\---------------\)
2. \(\left(x^{-1}\right)^{\frac{1}{2}}\\= x^{ -1 . \frac{1}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
3. \(\left(x^{\frac{5}{4}}\right)^{\frac{3}{4}}\\= x^{ \frac{5}{4} . \frac{3}{4} }= x^{\frac{15}{16}}\\=\sqrt[16]{ x^{15} }\\---------------\)
4. \(\left(x^{\frac{3}{4}}\right)^{\frac{3}{5}}\\= x^{ \frac{3}{4} . \frac{3}{5} }= x^{\frac{9}{20}}\\=\sqrt[20]{ x^{9} }\\---------------\)
5. \(\left(x^{\frac{-1}{6}}\right)^{\frac{4}{3}}\\= x^{ \frac{-1}{6} . \frac{4}{3} }= x^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ x^{2} }}=\frac{1}{\sqrt[9]{ x^{2} }}. \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x}\\---------------\)
6. \(\left(q^{\frac{2}{5}}\right)^{\frac{1}{6}}\\= q^{ \frac{2}{5} . \frac{1}{6} }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
7. \(\left(x^{\frac{-1}{5}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-1}{5} . (\frac{-1}{3}) }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
8. \(\left(x^{\frac{-3}{4}}\right)^{\frac{1}{2}}\\= x^{ \frac{-3}{4} . \frac{1}{2} }= x^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ x^{3} }}=\frac{1}{\sqrt[8]{ x^{3} }}. \color{purple}{\frac{\sqrt[8]{ x^{5} }}{\sqrt[8]{ x^{5} }}} \\=\frac{\sqrt[8]{ x^{5} }}{|x|}\\---------------\)
9. \(\left(q^{-2}\right)^{\frac{5}{3}}\\= q^{ -2 . \frac{5}{3} }= q^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ q^{10} }}\\=\frac{1}{q^{3}.\sqrt[3]{ q }}=\frac{1}{q^{3}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{4}}\\---------------\)
10. \(\left(q^{\frac{4}{5}}\right)^{\frac{4}{3}}\\= q^{ \frac{4}{5} . \frac{4}{3} }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
11. \(\left(x^{\frac{5}{2}}\right)^{\frac{1}{4}}\\= x^{ \frac{5}{2} . \frac{1}{4} }= x^{\frac{5}{8}}\\=\sqrt[8]{ x^{5} }\\---------------\)
12. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-2}{3} . (\frac{-1}{2}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)