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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-2}{5}}\right)^{\frac{1}{4}}\\= q^{ \frac{-2}{5} . \frac{1}{4} }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
2. \(\left(a^{\frac{1}{2}}\right)^{\frac{3}{4}}\\= a^{ \frac{1}{2} . \frac{3}{4} }= a^{\frac{3}{8}}\\=\sqrt[8]{ a^{3} }\\---------------\)
3. \(\left(q^{\frac{4}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{4}{5} . \frac{1}{3} }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
4. \(\left(x^{\frac{1}{4}}\right)^{\frac{-1}{4}}\\= x^{ \frac{1}{4} . (\frac{-1}{4}) }= x^{\frac{-1}{16}}\\=\frac{1}{\sqrt[16]{ x }}=\frac{1}{\sqrt[16]{ x }}. \color{purple}{\frac{\sqrt[16]{ x^{15} }}{\sqrt[16]{ x^{15} }}} \\=\frac{\sqrt[16]{ x^{15} }}{|x|}\\---------------\)
5. \(\left(q^{\frac{3}{5}}\right)^{\frac{-1}{5}}\\= q^{ \frac{3}{5} . (\frac{-1}{5}) }= q^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ q^{3} }}=\frac{1}{\sqrt[25]{ q^{3} }}. \color{purple}{\frac{\sqrt[25]{ q^{22} }}{\sqrt[25]{ q^{22} }}} \\=\frac{\sqrt[25]{ q^{22} }}{q}\\---------------\)
6. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-4}{5}}\\= q^{ \frac{-1}{6} . (\frac{-4}{5}) }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
7. \(\left(q^{\frac{5}{6}}\right)^{\frac{-1}{3}}\\= q^{ \frac{5}{6} . (\frac{-1}{3}) }= q^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ q^{5} }}=\frac{1}{\sqrt[18]{ q^{5} }}. \color{purple}{\frac{\sqrt[18]{ q^{13} }}{\sqrt[18]{ q^{13} }}} \\=\frac{\sqrt[18]{ q^{13} }}{|q|}\\---------------\)
8. \(\left(x^{\frac{-1}{3}}\right)^{1}\\= x^{ \frac{-1}{3} . 1 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
9. \(\left(a^{\frac{1}{3}}\right)^{2}\\= a^{ \frac{1}{3} . 2 }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
10. \(\left(q^{\frac{-4}{5}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-4}{5} . (\frac{-1}{5}) }= q^{\frac{4}{25}}\\=\sqrt[25]{ q^{4} }\\---------------\)
11. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-1}{3} . (\frac{-5}{4}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
12. \(\left(y^{\frac{4}{3}}\right)^{\frac{-1}{4}}\\= y^{ \frac{4}{3} . (\frac{-1}{4}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)