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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{2}}\right)^{\frac{3}{2}}\\= q^{ \frac{-1}{2} . \frac{3}{2} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
2. \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)
3. \(\left(q^{\frac{5}{6}}\right)^{\frac{4}{3}}\\= q^{ \frac{5}{6} . \frac{4}{3} }= q^{\frac{10}{9}}\\=\sqrt[9]{ q^{10} }=q.\sqrt[9]{ q }\\---------------\)
4. \(\left(y^{1}\right)^{\frac{4}{3}}\\= y^{ 1 . \frac{4}{3} }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
5. \(\left(a^{\frac{-5}{6}}\right)^{\frac{-5}{3}}\\= a^{ \frac{-5}{6} . (\frac{-5}{3}) }= a^{\frac{25}{18}}\\=\sqrt[18]{ a^{25} }=|a|.\sqrt[18]{ a^{7} }\\---------------\)
6. \(\left(a^{\frac{-5}{4}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-5}{4} . (\frac{-1}{2}) }= a^{\frac{5}{8}}\\=\sqrt[8]{ a^{5} }\\---------------\)
7. \(\left(q^{-1}\right)^{\frac{1}{2}}\\= q^{ -1 . \frac{1}{2} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
8. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{3} . \frac{1}{3} }= q^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ q }}=\frac{1}{\sqrt[9]{ q }}. \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q}\\---------------\)
9. \(\left(x^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{2}{3} . (\frac{-1}{2}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
10. \(\left(a^{-1}\right)^{1}\\= a^{ -1 . 1 }= a^{-1}\\=\frac{1}{a}\\---------------\)
11. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{1}{2} . \frac{1}{3} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
12. \(\left(y^{\frac{2}{3}}\right)^{\frac{4}{5}}\\= y^{ \frac{2}{3} . \frac{4}{5} }= y^{\frac{8}{15}}\\=\sqrt[15]{ y^{8} }\\---------------\)