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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-5}{4}}\right)^{-2}\\= x^{ \frac{-5}{4} . (-2) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
2. \(\left(a^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{-1}{3} . \frac{1}{2} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
3. \(\left(y^{\frac{1}{5}}\right)^{\frac{-1}{4}}\\= y^{ \frac{1}{5} . (\frac{-1}{4}) }= y^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ y }}=\frac{1}{\sqrt[20]{ y }}. \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y|}\\---------------\)
4. \(\left(y^{\frac{-1}{6}}\right)^{\frac{-1}{4}}\\= y^{ \frac{-1}{6} . (\frac{-1}{4}) }= y^{\frac{1}{24}}\\=\sqrt[24]{ y }\\---------------\)
5. \(\left(x^{-2}\right)^{\frac{3}{2}}\\= x^{ -2 . \frac{3}{2} }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)
6. \(\left(q^{\frac{5}{6}}\right)^{\frac{-1}{2}}\\= q^{ \frac{5}{6} . (\frac{-1}{2}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
7. \(\left(q^{\frac{-1}{2}}\right)^{\frac{5}{6}}\\= q^{ \frac{-1}{2} . \frac{5}{6} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
8. \(\left(y^{-1}\right)^{\frac{-5}{4}}\\= y^{ -1 . (\frac{-5}{4}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
9. \(\left(y^{\frac{-3}{5}}\right)^{-1}\\= y^{ \frac{-3}{5} . (-1) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
10. \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
11. \(\left(a^{\frac{5}{4}}\right)^{\frac{3}{5}}\\= a^{ \frac{5}{4} . \frac{3}{5} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
12. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-2}{5} . (\frac{-1}{2}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)