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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-2}{5} . (\frac{-1}{2}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
2. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-4}{3} . (\frac{-1}{2}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
3. \(\left(y^{\frac{1}{4}}\right)^{1}\\= y^{ \frac{1}{4} . 1 }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
4. \(\left(x^{\frac{1}{4}}\right)^{\frac{-4}{5}}\\= x^{ \frac{1}{4} . (\frac{-4}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
5. \(\left(q^{\frac{-1}{2}}\right)^{\frac{2}{3}}\\= q^{ \frac{-1}{2} . \frac{2}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
6. \(\left(q^{\frac{5}{6}}\right)^{\frac{1}{4}}\\= q^{ \frac{5}{6} . \frac{1}{4} }= q^{\frac{5}{24}}\\=\sqrt[24]{ q^{5} }\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{3}{4}}\\= a^{ -1 . \frac{3}{4} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
8. \(\left(y^{\frac{-1}{3}}\right)^{1}\\= y^{ \frac{-1}{3} . 1 }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
9. \(\left(y^{1}\right)^{\frac{2}{5}}\\= y^{ 1 . \frac{2}{5} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
10. \(\left(a^{\frac{1}{5}}\right)^{-2}\\= a^{ \frac{1}{5} . (-2) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
11. \(\left(x^{\frac{2}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{2}{5} . \frac{2}{3} }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
12. \(\left(q^{-2}\right)^{\frac{-1}{3}}\\= q^{ -2 . (\frac{-1}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)