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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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