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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{4}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{4}{5} . (\frac{-1}{2}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
2. \(\left(y^{\frac{3}{5}}\right)^{\frac{1}{5}}\\= y^{ \frac{3}{5} . \frac{1}{5} }= y^{\frac{3}{25}}\\=\sqrt[25]{ y^{3} }\\---------------\)
3. \(\left(y^{\frac{-3}{5}}\right)^{1}\\= y^{ \frac{-3}{5} . 1 }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
4. \(\left(y^{2}\right)^{\frac{2}{5}}\\= y^{ 2 . \frac{2}{5} }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
5. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{2} . (\frac{-1}{2}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
6. \(\left(x^{\frac{5}{6}}\right)^{\frac{-2}{5}}\\= x^{ \frac{5}{6} . (\frac{-2}{5}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
7. \(\left(y^{\frac{4}{3}}\right)^{\frac{5}{3}}\\= y^{ \frac{4}{3} . \frac{5}{3} }= y^{\frac{20}{9}}\\=\sqrt[9]{ y^{20} }=y^{2}.\sqrt[9]{ y^{2} }\\---------------\)
8. \(\left(q^{\frac{-2}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{-2}{5} . \frac{1}{3} }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
9. \(\left(x^{1}\right)^{\frac{-3}{5}}\\= x^{ 1 . (\frac{-3}{5}) }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
10. \(\left(a^{-1}\right)^{\frac{1}{3}}\\= a^{ -1 . \frac{1}{3} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
11. \(\left(a^{-1}\right)^{1}\\= a^{ -1 . 1 }= a^{-1}\\=\frac{1}{a}\\---------------\)
12. \(\left(a^{\frac{2}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{2}{3} . \frac{1}{2} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)