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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{5}}\right)^{\frac{-3}{2}}\\= a^{ \frac{1}{5} . (\frac{-3}{2}) }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
2. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-1}{6} . (\frac{-5}{4}) }= q^{\frac{5}{24}}\\=\sqrt[24]{ q^{5} }\\---------------\)
3. \(\left(a^{\frac{-1}{4}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{4} . (\frac{-1}{2}) }= a^{\frac{1}{8}}\\=\sqrt[8]{ a }\\---------------\)
4. \(\left(y^{\frac{2}{3}}\right)^{\frac{2}{5}}\\= y^{ \frac{2}{3} . \frac{2}{5} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
5. \(\left(a^{1}\right)^{\frac{1}{4}}\\= a^{ 1 . \frac{1}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
6. \(\left(q^{\frac{-3}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{-3}{2} . \frac{1}{2} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
7. \(\left(x^{\frac{-3}{2}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-3}{2} . (\frac{-3}{2}) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
8. \(\left(x^{\frac{1}{2}}\right)^{\frac{4}{3}}\\= x^{ \frac{1}{2} . \frac{4}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
9. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-1}{6} . (\frac{-1}{6}) }= q^{\frac{1}{36}}\\=\sqrt[36]{ q }\\---------------\)
10. \(\left(q^{\frac{5}{6}}\right)^{\frac{1}{2}}\\= q^{ \frac{5}{6} . \frac{1}{2} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
11. \(\left(a^{\frac{1}{4}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{4} . \frac{1}{2} }= a^{\frac{1}{8}}\\=\sqrt[8]{ a }\\---------------\)
12. \(\left(y^{\frac{1}{4}}\right)^{\frac{-1}{6}}\\= y^{ \frac{1}{4} . (\frac{-1}{6}) }= y^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ y }}=\frac{1}{\sqrt[24]{ y }}. \color{purple}{\frac{\sqrt[24]{ y^{23} }}{\sqrt[24]{ y^{23} }}} \\=\frac{\sqrt[24]{ y^{23} }}{|y|}\\---------------\)