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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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