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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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