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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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