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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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