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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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