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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-5}{4}}\right)^{\frac{5}{2}}\\= x^{ \frac{-5}{4} . \frac{5}{2} }= x^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ x^{25} }}\\=\frac{1}{|x^{3}|.\sqrt[8]{ x }}=\frac{1}{|x^{3}|.\sqrt[8]{ x }} \color{purple}{\frac{\sqrt[8]{ x^{7} }}{\sqrt[8]{ x^{7} }}} \\=\frac{\sqrt[8]{ x^{7} }}{|x^{4}|}\\---------------\)
2. \(\left(y^{\frac{3}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{3}{5} . (\frac{-1}{2}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
3. \(\left(q^{\frac{5}{3}}\right)^{\frac{-5}{6}}\\= q^{ \frac{5}{3} . (\frac{-5}{6}) }= q^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ q^{25} }}\\=\frac{1}{|q|.\sqrt[18]{ q^{7} }}=\frac{1}{|q|.\sqrt[18]{ q^{7} }} \color{purple}{\frac{\sqrt[18]{ q^{11} }}{\sqrt[18]{ q^{11} }}} \\=\frac{\sqrt[18]{ q^{11} }}{|q^{2}|}\\---------------\)
4. \(\left(a^{\frac{-1}{5}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-1}{5} . (\frac{-4}{3}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
5. \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{4}}\\= a^{ \frac{1}{2} . (\frac{-1}{4}) }= a^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ a }}=\frac{1}{\sqrt[8]{ a }}. \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a|}\\---------------\)
6. \(\left(a^{\frac{-1}{6}}\right)^{\frac{1}{2}}\\= a^{ \frac{-1}{6} . \frac{1}{2} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
7. \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{2}}\\= a^{ \frac{5}{6} . \frac{1}{2} }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
8. \(\left(a^{\frac{-5}{6}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-5}{6} . (\frac{-2}{3}) }= a^{\frac{5}{9}}\\=\sqrt[9]{ a^{5} }\\---------------\)
9. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{4}}\\= a^{ \frac{1}{3} . \frac{1}{4} }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
10. \(\left(a^{\frac{-1}{3}}\right)^{\frac{1}{6}}\\= a^{ \frac{-1}{3} . \frac{1}{6} }= a^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ a }}=\frac{1}{\sqrt[18]{ a }}. \color{purple}{\frac{\sqrt[18]{ a^{17} }}{\sqrt[18]{ a^{17} }}} \\=\frac{\sqrt[18]{ a^{17} }}{|a|}\\---------------\)
11. \(\left(q^{\frac{1}{3}}\right)^{\frac{-4}{3}}\\= q^{ \frac{1}{3} . (\frac{-4}{3}) }= q^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ q^{4} }}=\frac{1}{\sqrt[9]{ q^{4} }}. \color{purple}{\frac{\sqrt[9]{ q^{5} }}{\sqrt[9]{ q^{5} }}} \\=\frac{\sqrt[9]{ q^{5} }}{q}\\---------------\)
12. \(\left(x^{\frac{1}{2}}\right)^{\frac{-2}{5}}\\= x^{ \frac{1}{2} . (\frac{-2}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)