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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{2}{5}}\right)^{\frac{-1}{3}}\\= x^{ \frac{2}{5} . (\frac{-1}{3}) }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
2. \(\left(y^{\frac{-1}{3}}\right)^{1}\\= y^{ \frac{-1}{3} . 1 }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
3. \(\left(q^{1}\right)^{\frac{4}{3}}\\= q^{ 1 . \frac{4}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
4. \(\left(y^{\frac{1}{5}}\right)^{\frac{3}{2}}\\= y^{ \frac{1}{5} . \frac{3}{2} }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
5. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-1}{2} . (\frac{-4}{5}) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
6. \(\left(a^{\frac{3}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{3}{2} . \frac{1}{2} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
7. \(\left(y^{1}\right)^{\frac{-1}{4}}\\= y^{ 1 . (\frac{-1}{4}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
8. \(\left(x^{1}\right)^{\frac{5}{4}}\\= x^{ 1 . \frac{5}{4} }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
9. \(\left(y^{1}\right)^{\frac{1}{6}}\\= y^{ 1 . \frac{1}{6} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
10. \(\left(y^{-1}\right)^{\frac{1}{3}}\\= y^{ -1 . \frac{1}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
11. \(\left(y^{\frac{-5}{4}}\right)^{\frac{2}{3}}\\= y^{ \frac{-5}{4} . \frac{2}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
12. \(\left(a^{\frac{3}{5}}\right)^{\frac{1}{5}}\\= a^{ \frac{3}{5} . \frac{1}{5} }= a^{\frac{3}{25}}\\=\sqrt[25]{ a^{3} }\\---------------\)