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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{3}{2}}\right)^{\frac{-4}{5}}\\= q^{ \frac{3}{2} . (\frac{-4}{5}) }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
2. \(\left(x^{\frac{-1}{6}}\right)^{\frac{-1}{6}}\\= x^{ \frac{-1}{6} . (\frac{-1}{6}) }= x^{\frac{1}{36}}\\=\sqrt[36]{ x }\\---------------\)
3. \(\left(q^{\frac{-4}{5}}\right)^{-1}\\= q^{ \frac{-4}{5} . (-1) }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
4. \(\left(q^{-1}\right)^{\frac{-2}{3}}\\= q^{ -1 . (\frac{-2}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
5. \(\left(q^{\frac{3}{5}}\right)^{\frac{-4}{3}}\\= q^{ \frac{3}{5} . (\frac{-4}{3}) }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
6. \(\left(q^{\frac{-5}{3}}\right)^{-2}\\= q^{ \frac{-5}{3} . (-2) }= q^{\frac{10}{3}}\\=\sqrt[3]{ q^{10} }=q^{3}.\sqrt[3]{ q }\\---------------\)
7. \(\left(a^{\frac{-3}{5}}\right)^{1}\\= a^{ \frac{-3}{5} . 1 }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
8. \(\left(x^{\frac{-5}{6}}\right)^{\frac{4}{3}}\\= x^{ \frac{-5}{6} . \frac{4}{3} }= x^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ x^{10} }}\\=\frac{1}{x.\sqrt[9]{ x }}=\frac{1}{x.\sqrt[9]{ x }} \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x^{2}}\\---------------\)
9. \(\left(q^{-1}\right)^{\frac{-2}{5}}\\= q^{ -1 . (\frac{-2}{5}) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
10. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-3}{5}}\\= y^{ \frac{-1}{2} . (\frac{-3}{5}) }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
11. \(\left(q^{-1}\right)^{1}\\= q^{ -1 . 1 }= q^{-1}\\=\frac{1}{q}\\---------------\)
12. \(\left(q^{\frac{-1}{2}}\right)^{\frac{3}{4}}\\= q^{ \frac{-1}{2} . \frac{3}{4} }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}. \color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)