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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{-1}\\= q^{ 1 . (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
2. \(\left(y^{\frac{-1}{3}}\right)^{\frac{4}{5}}\\= y^{ \frac{-1}{3} . \frac{4}{5} }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
3. \(\left(q^{\frac{-4}{3}}\right)^{-2}\\= q^{ \frac{-4}{3} . (-2) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
4. \(\left(q^{\frac{5}{6}}\right)^{\frac{2}{3}}\\= q^{ \frac{5}{6} . \frac{2}{3} }= q^{\frac{5}{9}}\\=\sqrt[9]{ q^{5} }\\---------------\)
5. \(\left(y^{\frac{5}{2}}\right)^{\frac{5}{6}}\\= y^{ \frac{5}{2} . \frac{5}{6} }= y^{\frac{25}{12}}\\=\sqrt[12]{ y^{25} }=|y^{2}|.\sqrt[12]{ y }\\---------------\)
6. \(\left(x^{\frac{2}{5}}\right)^{\frac{-4}{5}}\\= x^{ \frac{2}{5} . (\frac{-4}{5}) }= x^{\frac{-8}{25}}\\=\frac{1}{\sqrt[25]{ x^{8} }}=\frac{1}{\sqrt[25]{ x^{8} }}. \color{purple}{\frac{\sqrt[25]{ x^{17} }}{\sqrt[25]{ x^{17} }}} \\=\frac{\sqrt[25]{ x^{17} }}{x}\\---------------\)
7. \(\left(x^{-2}\right)^{\frac{-1}{2}}\\= x^{ -2 . (\frac{-1}{2}) }= x^{1}\\\\---------------\)
8. \(\left(a^{1}\right)^{1}\\= a^{ 1 . 1 }= a^{1}\\\\---------------\)
9. \(\left(q^{\frac{1}{2}}\right)^{1}\\= q^{ \frac{1}{2} . 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
10. \(\left(a^{2}\right)^{1}\\= a^{ 2 . 1 }= a^{2}\\\\---------------\)
11. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-1}{3} . (\frac{-3}{2}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
12. \(\left(y^{\frac{-5}{3}}\right)^{\frac{1}{3}}\\= y^{ \frac{-5}{3} . \frac{1}{3} }= y^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ y^{5} }}=\frac{1}{\sqrt[9]{ y^{5} }}. \color{purple}{\frac{\sqrt[9]{ y^{4} }}{\sqrt[9]{ y^{4} }}} \\=\frac{\sqrt[9]{ y^{4} }}{y}\\---------------\)