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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{2}}\right)^{\frac{4}{3}}\\= q^{ \frac{-1}{2} . \frac{4}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
2. \(\left(y^{-1}\right)^{\frac{5}{6}}\\= y^{ -1 . \frac{5}{6} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
3. \(\left(a^{\frac{-1}{6}}\right)^{-2}\\= a^{ \frac{-1}{6} . (-2) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
4. \(\left(x^{\frac{-3}{2}}\right)^{\frac{5}{2}}\\= x^{ \frac{-3}{2} . \frac{5}{2} }= x^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ x^{15} }}\\=\frac{1}{|x^{3}|.\sqrt[4]{ x^{3} }}=\frac{1}{|x^{3}|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{4}|}\\---------------\)
5. \(\left(q^{\frac{5}{2}}\right)^{\frac{3}{2}}\\= q^{ \frac{5}{2} . \frac{3}{2} }= q^{\frac{15}{4}}\\=\sqrt[4]{ q^{15} }=|q^{3}|.\sqrt[4]{ q^{3} }\\---------------\)
6. \(\left(a^{\frac{-1}{3}}\right)^{1}\\= a^{ \frac{-1}{3} . 1 }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
7. \(\left(q^{\frac{3}{2}}\right)^{\frac{5}{2}}\\= q^{ \frac{3}{2} . \frac{5}{2} }= q^{\frac{15}{4}}\\=\sqrt[4]{ q^{15} }=|q^{3}|.\sqrt[4]{ q^{3} }\\---------------\)
8. \(\left(q^{\frac{-1}{3}}\right)^{\frac{5}{6}}\\= q^{ \frac{-1}{3} . \frac{5}{6} }= q^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ q^{5} }}=\frac{1}{\sqrt[18]{ q^{5} }}. \color{purple}{\frac{\sqrt[18]{ q^{13} }}{\sqrt[18]{ q^{13} }}} \\=\frac{\sqrt[18]{ q^{13} }}{|q|}\\---------------\)
9. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-3}{4}}\\= x^{ \frac{-2}{3} . (\frac{-3}{4}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
10. \(\left(q^{-1}\right)^{\frac{-2}{5}}\\= q^{ -1 . (\frac{-2}{5}) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
11. \(\left(q^{\frac{5}{2}}\right)^{-2}\\= q^{ \frac{5}{2} . (-2) }= q^{-5}\\=\frac{1}{q^{5}}\\---------------\)
12. \(\left(q^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{1}{3} . \frac{1}{2} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)