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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{5}{6}}\right)^{\frac{-5}{2}}\\= y^{ \frac{5}{6} . (\frac{-5}{2}) }= y^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ y^{25} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y }}=\frac{1}{|y^{2}|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{3}|}\\---------------\)
2. \(\left(y^{-1}\right)^{\frac{-2}{3}}\\= y^{ -1 . (\frac{-2}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
3. \(\left(q^{\frac{1}{2}}\right)^{\frac{5}{2}}\\= q^{ \frac{1}{2} . \frac{5}{2} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
4. \(\left(x^{\frac{2}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{2}{3} . \frac{2}{3} }= x^{\frac{4}{9}}\\=\sqrt[9]{ x^{4} }\\---------------\)
5. \(\left(x^{2}\right)^{\frac{-1}{6}}\\= x^{ 2 . (\frac{-1}{6}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
6. \(\left(y^{-1}\right)^{\frac{-1}{3}}\\= y^{ -1 . (\frac{-1}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
7. \(\left(q^{\frac{1}{6}}\right)^{\frac{-2}{5}}\\= q^{ \frac{1}{6} . (\frac{-2}{5}) }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
8. \(\left(q^{\frac{-2}{5}}\right)^{\frac{2}{3}}\\= q^{ \frac{-2}{5} . \frac{2}{3} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
9. \(\left(q^{-1}\right)^{\frac{-5}{3}}\\= q^{ -1 . (\frac{-5}{3}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
10. \(\left(a^{\frac{-3}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-3}{2} . (\frac{-1}{2}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
11. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-4}{5} . (\frac{-3}{4}) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
12. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{1}{2} . \frac{1}{3} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)