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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{2} . \frac{1}{2} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
2. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-4}{5}}\\= a^{ \frac{-5}{3} . (\frac{-4}{5}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
3. \(\left(x^{1}\right)^{-1}\\= x^{ 1 . (-1) }= x^{-1}\\=\frac{1}{x}\\---------------\)
4. \(\left(q^{\frac{5}{4}}\right)^{\frac{3}{4}}\\= q^{ \frac{5}{4} . \frac{3}{4} }= q^{\frac{15}{16}}\\=\sqrt[16]{ q^{15} }\\---------------\)
5. \(\left(x^{\frac{-1}{6}}\right)^{\frac{5}{3}}\\= x^{ \frac{-1}{6} . \frac{5}{3} }= x^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ x^{5} }}=\frac{1}{\sqrt[18]{ x^{5} }}. \color{purple}{\frac{\sqrt[18]{ x^{13} }}{\sqrt[18]{ x^{13} }}} \\=\frac{\sqrt[18]{ x^{13} }}{|x|}\\---------------\)
6. \(\left(q^{\frac{-3}{5}}\right)^{\frac{3}{2}}\\= q^{ \frac{-3}{5} . \frac{3}{2} }= q^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ q^{9} }}=\frac{1}{\sqrt[10]{ q^{9} }}. \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q|}\\---------------\)
7. \(\left(a^{\frac{4}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{4}{5} . \frac{1}{3} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
8. \(\left(a^{\frac{-5}{6}}\right)^{\frac{3}{2}}\\= a^{ \frac{-5}{6} . \frac{3}{2} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
9. \(\left(q^{\frac{5}{6}}\right)^{\frac{-5}{2}}\\= q^{ \frac{5}{6} . (\frac{-5}{2}) }= q^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ q^{25} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q }}=\frac{1}{|q^{2}|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{3}|}\\---------------\)
10. \(\left(x^{\frac{5}{2}}\right)^{\frac{1}{3}}\\= x^{ \frac{5}{2} . \frac{1}{3} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
11. \(\left(x^{\frac{-1}{6}}\right)^{\frac{5}{6}}\\= x^{ \frac{-1}{6} . \frac{5}{6} }= x^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ x^{5} }}=\frac{1}{\sqrt[36]{ x^{5} }}. \color{purple}{\frac{\sqrt[36]{ x^{31} }}{\sqrt[36]{ x^{31} }}} \\=\frac{\sqrt[36]{ x^{31} }}{|x|}\\---------------\)
12. \(\left(y^{\frac{2}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{2}{3} . \frac{1}{2} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)