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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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