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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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