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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-5}{4}}\right)^{-1}\\= a^{ \frac{-5}{4} . (-1) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
2. \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
3. \(\left(y^{\frac{4}{5}}\right)^{-2}\\= y^{ \frac{4}{5} . (-2) }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)
4. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{6}}\\= q^{ \frac{-1}{3} . \frac{1}{6} }= q^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ q }}=\frac{1}{\sqrt[18]{ q }}. \color{purple}{\frac{\sqrt[18]{ q^{17} }}{\sqrt[18]{ q^{17} }}} \\=\frac{\sqrt[18]{ q^{17} }}{|q|}\\---------------\)
5. \(\left(x^{\frac{2}{3}}\right)^{\frac{2}{5}}\\= x^{ \frac{2}{3} . \frac{2}{5} }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
6. \(\left(y^{\frac{1}{6}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{6} . (\frac{-1}{2}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
7. \(\left(y^{\frac{1}{6}}\right)^{\frac{5}{3}}\\= y^{ \frac{1}{6} . \frac{5}{3} }= y^{\frac{5}{18}}\\=\sqrt[18]{ y^{5} }\\---------------\)
8. \(\left(q^{\frac{-4}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{-4}{5} . \frac{1}{3} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
9. \(\left(x^{1}\right)^{\frac{-3}{4}}\\= x^{ 1 . (\frac{-3}{4}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
10. \(\left(a^{\frac{3}{4}}\right)^{-1}\\= a^{ \frac{3}{4} . (-1) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
11. \(\left(q^{\frac{2}{5}}\right)^{\frac{1}{6}}\\= q^{ \frac{2}{5} . \frac{1}{6} }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
12. \(\left(y^{\frac{-1}{2}}\right)^{-1}\\= y^{ \frac{-1}{2} . (-1) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)