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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-1}{2} . (\frac{-5}{2}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
2. \(\left(q^{\frac{-3}{4}}\right)^{-1}\\= q^{ \frac{-3}{4} . (-1) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
3. \(\left(a^{\frac{-1}{2}}\right)^{\frac{1}{6}}\\= a^{ \frac{-1}{2} . \frac{1}{6} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
4. \(\left(a^{\frac{3}{5}}\right)^{\frac{-4}{5}}\\= a^{ \frac{3}{5} . (\frac{-4}{5}) }= a^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ a^{12} }}=\frac{1}{\sqrt[25]{ a^{12} }}. \color{purple}{\frac{\sqrt[25]{ a^{13} }}{\sqrt[25]{ a^{13} }}} \\=\frac{\sqrt[25]{ a^{13} }}{a}\\---------------\)
5. \(\left(y^{\frac{-4}{3}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-4}{3} . (\frac{-2}{3}) }= y^{\frac{8}{9}}\\=\sqrt[9]{ y^{8} }\\---------------\)
6. \(\left(q^{\frac{-2}{3}}\right)^{-1}\\= q^{ \frac{-2}{3} . (-1) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
7. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-1}{6} . (\frac{-2}{3}) }= q^{\frac{1}{9}}\\=\sqrt[9]{ q }\\---------------\)
8. \(\left(y^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{1}{3} . \frac{1}{2} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
9. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-1}{2} . (\frac{-1}{5}) }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
10. \(\left(q^{1}\right)^{\frac{4}{5}}\\= q^{ 1 . \frac{4}{5} }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
11. \(\left(q^{\frac{3}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{3}{5} . (\frac{-1}{2}) }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)
12. \(\left(q^{-1}\right)^{\frac{3}{4}}\\= q^{ -1 . \frac{3}{4} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)