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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{5}}\right)^{\frac{5}{4}}\\= q^{ \frac{1}{5} . \frac{5}{4} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
2. \(\left(x^{-1}\right)^{\frac{1}{4}}\\= x^{ -1 . \frac{1}{4} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
3. \(\left(a^{\frac{1}{6}}\right)^{\frac{-4}{3}}\\= a^{ \frac{1}{6} . (\frac{-4}{3}) }= a^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ a^{2} }}=\frac{1}{\sqrt[9]{ a^{2} }}. \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a}\\---------------\)
4. \(\left(y^{\frac{5}{2}}\right)^{\frac{-3}{2}}\\= y^{ \frac{5}{2} . (\frac{-3}{2}) }= y^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ y^{15} }}\\=\frac{1}{|y^{3}|.\sqrt[4]{ y^{3} }}=\frac{1}{|y^{3}|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{4}|}\\---------------\)
5. \(\left(a^{\frac{-3}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-3}{2} . (\frac{-1}{2}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
6. \(\left(q^{\frac{-5}{6}}\right)^{\frac{2}{5}}\\= q^{ \frac{-5}{6} . \frac{2}{5} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
7. \(\left(q^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{1}{3} . \frac{1}{2} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
8. \(\left(a^{\frac{5}{6}}\right)^{\frac{5}{3}}\\= a^{ \frac{5}{6} . \frac{5}{3} }= a^{\frac{25}{18}}\\=\sqrt[18]{ a^{25} }=|a|.\sqrt[18]{ a^{7} }\\---------------\)
9. \(\left(q^{\frac{5}{4}}\right)^{\frac{-1}{2}}\\= q^{ \frac{5}{4} . (\frac{-1}{2}) }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
10. \(\left(y^{\frac{3}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{3}{2} . \frac{1}{3} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
11. \(\left(y^{\frac{-3}{5}}\right)^{\frac{2}{5}}\\= y^{ \frac{-3}{5} . \frac{2}{5} }= y^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ y^{6} }}=\frac{1}{\sqrt[25]{ y^{6} }}. \color{purple}{\frac{\sqrt[25]{ y^{19} }}{\sqrt[25]{ y^{19} }}} \\=\frac{\sqrt[25]{ y^{19} }}{y}\\---------------\)
12. \(\left(a^{\frac{5}{6}}\right)^{\frac{-5}{6}}\\= a^{ \frac{5}{6} . (\frac{-5}{6}) }= a^{\frac{-25}{36}}\\=\frac{1}{\sqrt[36]{ a^{25} }}=\frac{1}{\sqrt[36]{ a^{25} }}. \color{purple}{\frac{\sqrt[36]{ a^{11} }}{\sqrt[36]{ a^{11} }}} \\=\frac{\sqrt[36]{ a^{11} }}{|a|}\\---------------\)