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Werk uit m.b.v. de rekenregels

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

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