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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{1}\right)^{\frac{1}{3}}\\= a^{ 1 . \frac{1}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
2. \(\left(q^{\frac{2}{3}}\right)^{\frac{-1}{4}}\\= q^{ \frac{2}{3} . (\frac{-1}{4}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{1}\\= a^{ \frac{-1}{3} . 1 }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
4. \(\left(q^{-1}\right)^{-1}\\= q^{ -1 . (-1) }= q^{1}\\\\---------------\)
5. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-3}{4} . (\frac{-1}{6}) }= a^{\frac{1}{8}}\\=\sqrt[8]{ a }\\---------------\)
6. \(\left(y^{\frac{2}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{2}{5} . (\frac{-1}{2}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
7. \(\left(a^{1}\right)^{\frac{-4}{3}}\\= a^{ 1 . (\frac{-4}{3}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
8. \(\left(y^{\frac{-5}{6}}\right)^{\frac{1}{3}}\\= y^{ \frac{-5}{6} . \frac{1}{3} }= y^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ y^{5} }}=\frac{1}{\sqrt[18]{ y^{5} }}. \color{purple}{\frac{\sqrt[18]{ y^{13} }}{\sqrt[18]{ y^{13} }}} \\=\frac{\sqrt[18]{ y^{13} }}{|y|}\\---------------\)
9. \(\left(x^{\frac{5}{2}}\right)^{-2}\\= x^{ \frac{5}{2} . (-2) }= x^{-5}\\=\frac{1}{x^{5}}\\---------------\)
10. \(\left(y^{1}\right)^{\frac{4}{5}}\\= y^{ 1 . \frac{4}{5} }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
11. \(\left(a^{\frac{-1}{6}}\right)^{\frac{2}{5}}\\= a^{ \frac{-1}{6} . \frac{2}{5} }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
12. \(\left(x^{\frac{-5}{4}}\right)^{\frac{1}{3}}\\= x^{ \frac{-5}{4} . \frac{1}{3} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)