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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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