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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{5} . \frac{1}{2} }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
2. \(\left(a^{\frac{-1}{4}}\right)^{-1}\\= a^{ \frac{-1}{4} . (-1) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
3. \(\left(y^{\frac{1}{2}}\right)^{-2}\\= y^{ \frac{1}{2} . (-2) }= y^{-1}\\=\frac{1}{y}\\---------------\)
4. \(\left(y^{\frac{4}{3}}\right)^{\frac{-5}{4}}\\= y^{ \frac{4}{3} . (\frac{-5}{4}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
5. \(\left(a^{\frac{-1}{2}}\right)^{\frac{3}{4}}\\= a^{ \frac{-1}{2} . \frac{3}{4} }= a^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ a^{3} }}=\frac{1}{\sqrt[8]{ a^{3} }}. \color{purple}{\frac{\sqrt[8]{ a^{5} }}{\sqrt[8]{ a^{5} }}} \\=\frac{\sqrt[8]{ a^{5} }}{|a|}\\---------------\)
6. \(\left(a^{\frac{-1}{6}}\right)^{\frac{3}{5}}\\= a^{ \frac{-1}{6} . \frac{3}{5} }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
7. \(\left(x^{\frac{-2}{5}}\right)^{\frac{1}{3}}\\= x^{ \frac{-2}{5} . \frac{1}{3} }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
8. \(\left(q^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{-2}{3} . \frac{1}{2} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
9. \(\left(a^{-1}\right)^{\frac{-1}{3}}\\= a^{ -1 . (\frac{-1}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
10. \(\left(x^{\frac{5}{6}}\right)^{\frac{-1}{3}}\\= x^{ \frac{5}{6} . (\frac{-1}{3}) }= x^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ x^{5} }}=\frac{1}{\sqrt[18]{ x^{5} }}. \color{purple}{\frac{\sqrt[18]{ x^{13} }}{\sqrt[18]{ x^{13} }}} \\=\frac{\sqrt[18]{ x^{13} }}{|x|}\\---------------\)
11. \(\left(y^{-1}\right)^{\frac{1}{3}}\\= y^{ -1 . \frac{1}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
12. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-2}{5}}\\= y^{ \frac{-1}{3} . (\frac{-2}{5}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)