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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{3}}\right)^{-1}\\= a^{ \frac{1}{3} . (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
2. \(\left(q^{\frac{2}{3}}\right)^{\frac{-2}{3}}\\= q^{ \frac{2}{3} . (\frac{-2}{3}) }= q^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ q^{4} }}=\frac{1}{\sqrt[9]{ q^{4} }}. \color{purple}{\frac{\sqrt[9]{ q^{5} }}{\sqrt[9]{ q^{5} }}} \\=\frac{\sqrt[9]{ q^{5} }}{q}\\---------------\)
3. \(\left(a^{1}\right)^{\frac{1}{4}}\\= a^{ 1 . \frac{1}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
4. \(\left(a^{-1}\right)^{\frac{-3}{2}}\\= a^{ -1 . (\frac{-3}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
5. \(\left(x^{1}\right)^{\frac{-5}{6}}\\= x^{ 1 . (\frac{-5}{6}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
6. \(\left(q^{\frac{5}{3}}\right)^{\frac{2}{5}}\\= q^{ \frac{5}{3} . \frac{2}{5} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
7. \(\left(a^{\frac{-1}{4}}\right)^{\frac{1}{2}}\\= a^{ \frac{-1}{4} . \frac{1}{2} }= a^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ a }}=\frac{1}{\sqrt[8]{ a }}. \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a|}\\---------------\)
8. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{5} . (\frac{-1}{2}) }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
9. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{2} . \frac{1}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
10. \(\left(x^{\frac{1}{2}}\right)^{\frac{-5}{3}}\\= x^{ \frac{1}{2} . (\frac{-5}{3}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
11. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-1}{4}}\\= y^{ \frac{-1}{5} . (\frac{-1}{4}) }= y^{\frac{1}{20}}\\=\sqrt[20]{ y }\\---------------\)
12. \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)