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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{5}}\right)^{\frac{1}{6}}\\= q^{ \frac{1}{5} . \frac{1}{6} }= q^{\frac{1}{30}}\\=\sqrt[30]{ q }\\---------------\)
2. \(\left(x^{\frac{5}{3}}\right)^{-1}\\= x^{ \frac{5}{3} . (-1) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
3. \(\left(y^{\frac{2}{3}}\right)^{\frac{-5}{6}}\\= y^{ \frac{2}{3} . (\frac{-5}{6}) }= y^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ y^{5} }}=\frac{1}{\sqrt[9]{ y^{5} }}. \color{purple}{\frac{\sqrt[9]{ y^{4} }}{\sqrt[9]{ y^{4} }}} \\=\frac{\sqrt[9]{ y^{4} }}{y}\\---------------\)
4. \(\left(x^{\frac{3}{5}}\right)^{\frac{1}{4}}\\= x^{ \frac{3}{5} . \frac{1}{4} }= x^{\frac{3}{20}}\\=\sqrt[20]{ x^{3} }\\---------------\)
5. \(\left(x^{\frac{-1}{6}}\right)^{-1}\\= x^{ \frac{-1}{6} . (-1) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
6. \(\left(a^{\frac{-5}{6}}\right)^{\frac{-4}{5}}\\= a^{ \frac{-5}{6} . (\frac{-4}{5}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
7. \(\left(q^{\frac{2}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{2}{3} . (\frac{-1}{3}) }= q^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ q^{2} }}=\frac{1}{\sqrt[9]{ q^{2} }}. \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q}\\---------------\)
8. \(\left(q^{\frac{-5}{4}}\right)^{\frac{3}{4}}\\= q^{ \frac{-5}{4} . \frac{3}{4} }= q^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ q^{15} }}=\frac{1}{\sqrt[16]{ q^{15} }}. \color{purple}{\frac{\sqrt[16]{ q }}{\sqrt[16]{ q }}} \\=\frac{\sqrt[16]{ q }}{|q|}\\---------------\)
9. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-5}{3} . (\frac{-1}{2}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
10. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-1}{5} . (\frac{-1}{3}) }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
11. \(\left(q^{\frac{4}{3}}\right)^{\frac{3}{2}}\\= q^{ \frac{4}{3} . \frac{3}{2} }= q^{2}\\\\---------------\)
12. \(\left(a^{-1}\right)^{1}\\= a^{ -1 . 1 }= a^{-1}\\=\frac{1}{a}\\---------------\)