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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{2}\right)^{\frac{1}{4}}\\= a^{ 2 . \frac{1}{4} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
2. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-5}{6} . (\frac{-1}{3}) }= q^{\frac{5}{18}}\\=\sqrt[18]{ q^{5} }\\---------------\)
3. \(\left(x^{\frac{5}{4}}\right)^{\frac{-1}{5}}\\= x^{ \frac{5}{4} . (\frac{-1}{5}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
4. \(\left(y^{\frac{1}{2}}\right)^{\frac{2}{5}}\\= y^{ \frac{1}{2} . \frac{2}{5} }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
5. \(\left(y^{\frac{5}{3}}\right)^{\frac{-3}{5}}\\= y^{ \frac{5}{3} . (\frac{-3}{5}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
6. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-2}{3} . (\frac{-5}{3}) }= q^{\frac{10}{9}}\\=\sqrt[9]{ q^{10} }=q.\sqrt[9]{ q }\\---------------\)
7. \(\left(y^{2}\right)^{\frac{-2}{5}}\\= y^{ 2 . (\frac{-2}{5}) }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
8. \(\left(x^{\frac{3}{5}}\right)^{\frac{-1}{5}}\\= x^{ \frac{3}{5} . (\frac{-1}{5}) }= x^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ x^{3} }}=\frac{1}{\sqrt[25]{ x^{3} }}. \color{purple}{\frac{\sqrt[25]{ x^{22} }}{\sqrt[25]{ x^{22} }}} \\=\frac{\sqrt[25]{ x^{22} }}{x}\\---------------\)
9. \(\left(y^{\frac{1}{2}}\right)^{\frac{-5}{4}}\\= y^{ \frac{1}{2} . (\frac{-5}{4}) }= y^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ y^{5} }}=\frac{1}{\sqrt[8]{ y^{5} }}. \color{purple}{\frac{\sqrt[8]{ y^{3} }}{\sqrt[8]{ y^{3} }}} \\=\frac{\sqrt[8]{ y^{3} }}{|y|}\\---------------\)
10. \(\left(q^{-1}\right)^{\frac{3}{4}}\\= q^{ -1 . \frac{3}{4} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
11. \(\left(x^{\frac{5}{4}}\right)^{\frac{-5}{2}}\\= x^{ \frac{5}{4} . (\frac{-5}{2}) }= x^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ x^{25} }}\\=\frac{1}{|x^{3}|.\sqrt[8]{ x }}=\frac{1}{|x^{3}|.\sqrt[8]{ x }} \color{purple}{\frac{\sqrt[8]{ x^{7} }}{\sqrt[8]{ x^{7} }}} \\=\frac{\sqrt[8]{ x^{7} }}{|x^{4}|}\\---------------\)
12. \(\left(q^{\frac{1}{3}}\right)^{\frac{-4}{3}}\\= q^{ \frac{1}{3} . (\frac{-4}{3}) }= q^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ q^{4} }}=\frac{1}{\sqrt[9]{ q^{4} }}. \color{purple}{\frac{\sqrt[9]{ q^{5} }}{\sqrt[9]{ q^{5} }}} \\=\frac{\sqrt[9]{ q^{5} }}{q}\\---------------\)