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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-1}\right)^{\frac{-1}{2}}\\= q^{ -1 . (\frac{-1}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
2. \(\left(y^{\frac{-5}{2}}\right)^{-1}\\= y^{ \frac{-5}{2} . (-1) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
3. \(\left(y^{-2}\right)^{\frac{-1}{5}}\\= y^{ -2 . (\frac{-1}{5}) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
4. \(\left(y^{-1}\right)^{\frac{3}{5}}\\= y^{ -1 . \frac{3}{5} }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
5. \(\left(q^{\frac{-4}{3}}\right)^{\frac{4}{3}}\\= q^{ \frac{-4}{3} . \frac{4}{3} }= q^{\frac{-16}{9}}\\=\frac{1}{\sqrt[9]{ q^{16} }}\\=\frac{1}{q.\sqrt[9]{ q^{7} }}=\frac{1}{q.\sqrt[9]{ q^{7} }} \color{purple}{\frac{\sqrt[9]{ q^{2} }}{\sqrt[9]{ q^{2} }}} \\=\frac{\sqrt[9]{ q^{2} }}{q^{2}}\\---------------\)
6. \(\left(x^{\frac{2}{5}}\right)^{\frac{-4}{3}}\\= x^{ \frac{2}{5} . (\frac{-4}{3}) }= x^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ x^{8} }}=\frac{1}{\sqrt[15]{ x^{8} }}. \color{purple}{\frac{\sqrt[15]{ x^{7} }}{\sqrt[15]{ x^{7} }}} \\=\frac{\sqrt[15]{ x^{7} }}{x}\\---------------\)
7. \(\left(y^{\frac{1}{2}}\right)^{-2}\\= y^{ \frac{1}{2} . (-2) }= y^{-1}\\=\frac{1}{y}\\---------------\)
8. \(\left(y^{\frac{-4}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{-4}{3} . \frac{1}{2} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
9. \(\left(y^{\frac{4}{3}}\right)^{\frac{-2}{3}}\\= y^{ \frac{4}{3} . (\frac{-2}{3}) }= y^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ y^{8} }}=\frac{1}{\sqrt[9]{ y^{8} }}. \color{purple}{\frac{\sqrt[9]{ y }}{\sqrt[9]{ y }}} \\=\frac{\sqrt[9]{ y }}{y}\\---------------\)
10. \(\left(x^{\frac{5}{3}}\right)^{\frac{-2}{5}}\\= x^{ \frac{5}{3} . (\frac{-2}{5}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
11. \(\left(y^{\frac{1}{5}}\right)^{\frac{1}{4}}\\= y^{ \frac{1}{5} . \frac{1}{4} }= y^{\frac{1}{20}}\\=\sqrt[20]{ y }\\---------------\)
12. \(\left(a^{\frac{-1}{2}}\right)^{2}\\= a^{ \frac{-1}{2} . 2 }= a^{-1}\\=\frac{1}{a}\\---------------\)