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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{1}\right)^{\frac{1}{3}}\\= y^{ 1 . \frac{1}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
2. \(\left(y^{\frac{-3}{2}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-3}{2} . (\frac{-1}{3}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
3. \(\left(a^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= a^{ \frac{-1}{2} . \frac{1}{3} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
4. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-3}{5} . (\frac{-2}{3}) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
5. \(\left(a^{\frac{2}{5}}\right)^{\frac{-1}{4}}\\= a^{ \frac{2}{5} . (\frac{-1}{4}) }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
6. \(\left(q^{\frac{5}{4}}\right)^{1}\\= q^{ \frac{5}{4} . 1 }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
7. \(\left(q^{\frac{-4}{5}}\right)^{-2}\\= q^{ \frac{-4}{5} . (-2) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
8. \(\left(x^{\frac{1}{2}}\right)^{\frac{4}{5}}\\= x^{ \frac{1}{2} . \frac{4}{5} }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
9. \(\left(q^{2}\right)^{\frac{-2}{3}}\\= q^{ 2 . (\frac{-2}{3}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
10. \(\left(q^{\frac{-5}{6}}\right)^{\frac{1}{3}}\\= q^{ \frac{-5}{6} . \frac{1}{3} }= q^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ q^{5} }}=\frac{1}{\sqrt[18]{ q^{5} }}. \color{purple}{\frac{\sqrt[18]{ q^{13} }}{\sqrt[18]{ q^{13} }}} \\=\frac{\sqrt[18]{ q^{13} }}{|q|}\\---------------\)
11. \(\left(q^{\frac{1}{4}}\right)^{\frac{-3}{4}}\\= q^{ \frac{1}{4} . (\frac{-3}{4}) }= q^{\frac{-3}{16}}\\=\frac{1}{\sqrt[16]{ q^{3} }}=\frac{1}{\sqrt[16]{ q^{3} }}. \color{purple}{\frac{\sqrt[16]{ q^{13} }}{\sqrt[16]{ q^{13} }}} \\=\frac{\sqrt[16]{ q^{13} }}{|q|}\\---------------\)
12. \(\left(x^{\frac{-3}{4}}\right)^{\frac{-1}{6}}\\= x^{ \frac{-3}{4} . (\frac{-1}{6}) }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)