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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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