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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-1}{5}}\\= x^{ \frac{-1}{2} . (\frac{-1}{5}) }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
2. \(\left(y^{\frac{5}{4}}\right)^{\frac{-4}{3}}\\= y^{ \frac{5}{4} . (\frac{-4}{3}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
3. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{3} . (\frac{-1}{2}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
4. \(\left(q^{\frac{5}{4}}\right)^{\frac{-1}{6}}\\= q^{ \frac{5}{4} . (\frac{-1}{6}) }= q^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ q^{5} }}=\frac{1}{\sqrt[24]{ q^{5} }}. \color{purple}{\frac{\sqrt[24]{ q^{19} }}{\sqrt[24]{ q^{19} }}} \\=\frac{\sqrt[24]{ q^{19} }}{|q|}\\---------------\)
5. \(\left(a^{\frac{2}{3}}\right)^{\frac{-5}{3}}\\= a^{ \frac{2}{3} . (\frac{-5}{3}) }= a^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ a^{10} }}\\=\frac{1}{a.\sqrt[9]{ a }}=\frac{1}{a.\sqrt[9]{ a }} \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a^{2}}\\---------------\)
6. \(\left(y^{\frac{-5}{3}}\right)^{\frac{5}{6}}\\= y^{ \frac{-5}{3} . \frac{5}{6} }= y^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ y^{25} }}\\=\frac{1}{|y|.\sqrt[18]{ y^{7} }}=\frac{1}{|y|.\sqrt[18]{ y^{7} }} \color{purple}{\frac{\sqrt[18]{ y^{11} }}{\sqrt[18]{ y^{11} }}} \\=\frac{\sqrt[18]{ y^{11} }}{|y^{2}|}\\---------------\)
7. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-5}{2}}\\= x^{ \frac{-5}{6} . (\frac{-5}{2}) }= x^{\frac{25}{12}}\\=\sqrt[12]{ x^{25} }=|x^{2}|.\sqrt[12]{ x }\\---------------\)
8. \(\left(a^{\frac{1}{6}}\right)^{\frac{-1}{6}}\\= a^{ \frac{1}{6} . (\frac{-1}{6}) }= a^{\frac{-1}{36}}\\=\frac{1}{\sqrt[36]{ a }}=\frac{1}{\sqrt[36]{ a }}. \color{purple}{\frac{\sqrt[36]{ a^{35} }}{\sqrt[36]{ a^{35} }}} \\=\frac{\sqrt[36]{ a^{35} }}{|a|}\\---------------\)
9. \(\left(q^{\frac{-5}{4}}\right)^{-1}\\= q^{ \frac{-5}{4} . (-1) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
10. \(\left(y^{\frac{2}{3}}\right)^{\frac{5}{3}}\\= y^{ \frac{2}{3} . \frac{5}{3} }= y^{\frac{10}{9}}\\=\sqrt[9]{ y^{10} }=y.\sqrt[9]{ y }\\---------------\)
11. \(\left(x^{\frac{5}{4}}\right)^{\frac{-3}{2}}\\= x^{ \frac{5}{4} . (\frac{-3}{2}) }= x^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ x^{15} }}\\=\frac{1}{|x|.\sqrt[8]{ x^{7} }}=\frac{1}{|x|.\sqrt[8]{ x^{7} }} \color{purple}{\frac{\sqrt[8]{ x }}{\sqrt[8]{ x }}} \\=\frac{\sqrt[8]{ x }}{|x^{2}|}\\---------------\)
12. \(\left(y^{\frac{1}{2}}\right)^{\frac{2}{3}}\\= y^{ \frac{1}{2} . \frac{2}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)