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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{2}}\right)^{\frac{3}{5}}\\= x^{ \frac{-1}{2} . \frac{3}{5} }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
2. \(\left(q^{\frac{-5}{4}}\right)^{\frac{1}{6}}\\= q^{ \frac{-5}{4} . \frac{1}{6} }= q^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ q^{5} }}=\frac{1}{\sqrt[24]{ q^{5} }}. \color{purple}{\frac{\sqrt[24]{ q^{19} }}{\sqrt[24]{ q^{19} }}} \\=\frac{\sqrt[24]{ q^{19} }}{|q|}\\---------------\)
3. \(\left(q^{\frac{5}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{5}{3} . \frac{1}{2} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
4. \(\left(a^{\frac{-5}{4}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-5}{4} . (\frac{-1}{2}) }= a^{\frac{5}{8}}\\=\sqrt[8]{ a^{5} }\\---------------\)
5. \(\left(x^{\frac{5}{2}}\right)^{\frac{-1}{2}}\\= x^{ \frac{5}{2} . (\frac{-1}{2}) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
6. \(\left(a^{\frac{4}{3}}\right)^{\frac{-5}{3}}\\= a^{ \frac{4}{3} . (\frac{-5}{3}) }= a^{\frac{-20}{9}}\\=\frac{1}{\sqrt[9]{ a^{20} }}\\=\frac{1}{a^{2}.\sqrt[9]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[9]{ a^{2} }} \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a^{3}}\\---------------\)
7. \(\left(q^{\frac{-1}{2}}\right)^{\frac{2}{3}}\\= q^{ \frac{-1}{2} . \frac{2}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
8. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-2}{5} . (\frac{-1}{2}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
9. \(\left(a^{\frac{-4}{5}}\right)^{\frac{3}{5}}\\= a^{ \frac{-4}{5} . \frac{3}{5} }= a^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ a^{12} }}=\frac{1}{\sqrt[25]{ a^{12} }}. \color{purple}{\frac{\sqrt[25]{ a^{13} }}{\sqrt[25]{ a^{13} }}} \\=\frac{\sqrt[25]{ a^{13} }}{a}\\---------------\)
10. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-1}{3} . (\frac{-5}{2}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
11. \(\left(q^{\frac{4}{5}}\right)^{\frac{1}{2}}\\= q^{ \frac{4}{5} . \frac{1}{2} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
12. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-1}{2} . (\frac{-2}{5}) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)