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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{6}}\right)^{\frac{-3}{5}}\\= x^{ \frac{-1}{6} . (\frac{-3}{5}) }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
2. \(\left(q^{\frac{5}{6}}\right)^{1}\\= q^{ \frac{5}{6} . 1 }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
3. \(\left(a^{\frac{5}{3}}\right)^{\frac{4}{3}}\\= a^{ \frac{5}{3} . \frac{4}{3} }= a^{\frac{20}{9}}\\=\sqrt[9]{ a^{20} }=a^{2}.\sqrt[9]{ a^{2} }\\---------------\)
4. \(\left(y^{\frac{-1}{4}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-1}{4} . (\frac{-1}{3}) }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
5. \(\left(x^{\frac{1}{6}}\right)^{1}\\= x^{ \frac{1}{6} . 1 }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
6. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-2}{5} . (\frac{-3}{4}) }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
7. \(\left(a^{-1}\right)^{1}\\= a^{ -1 . 1 }= a^{-1}\\=\frac{1}{a}\\---------------\)
8. \(\left(x^{-1}\right)^{-2}\\= x^{ -1 . (-2) }= x^{2}\\\\---------------\)
9. \(\left(x^{\frac{1}{6}}\right)^{\frac{-1}{3}}\\= x^{ \frac{1}{6} . (\frac{-1}{3}) }= x^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ x }}=\frac{1}{\sqrt[18]{ x }}. \color{purple}{\frac{\sqrt[18]{ x^{17} }}{\sqrt[18]{ x^{17} }}} \\=\frac{\sqrt[18]{ x^{17} }}{|x|}\\---------------\)
10. \(\left(q^{\frac{5}{4}}\right)^{\frac{1}{4}}\\= q^{ \frac{5}{4} . \frac{1}{4} }= q^{\frac{5}{16}}\\=\sqrt[16]{ q^{5} }\\---------------\)
11. \(\left(q^{\frac{3}{4}}\right)^{\frac{-1}{2}}\\= q^{ \frac{3}{4} . (\frac{-1}{2}) }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}. \color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)
12. \(\left(y^{\frac{-1}{3}}\right)^{-1}\\= y^{ \frac{-1}{3} . (-1) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)