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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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