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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-5}{6} . (\frac{-1}{2}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
2. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-1}{3} . (\frac{-1}{3}) }= a^{\frac{1}{9}}\\=\sqrt[9]{ a }\\---------------\)
3. \(\left(y^{\frac{1}{3}}\right)^{\frac{4}{5}}\\= y^{ \frac{1}{3} . \frac{4}{5} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
4. \(\left(a^{\frac{1}{2}}\right)^{\frac{1}{4}}\\= a^{ \frac{1}{2} . \frac{1}{4} }= a^{\frac{1}{8}}\\=\sqrt[8]{ a }\\---------------\)
5. \(\left(y^{\frac{3}{5}}\right)^{-1}\\= y^{ \frac{3}{5} . (-1) }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
6. \(\left(a^{\frac{-3}{5}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-3}{5} . (\frac{-1}{3}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
7. \(\left(q^{\frac{4}{5}}\right)^{\frac{-1}{5}}\\= q^{ \frac{4}{5} . (\frac{-1}{5}) }= q^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ q^{4} }}=\frac{1}{\sqrt[25]{ q^{4} }}. \color{purple}{\frac{\sqrt[25]{ q^{21} }}{\sqrt[25]{ q^{21} }}} \\=\frac{\sqrt[25]{ q^{21} }}{q}\\---------------\)
8. \(\left(y^{\frac{1}{3}}\right)^{\frac{-5}{4}}\\= y^{ \frac{1}{3} . (\frac{-5}{4}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
9. \(\left(q^{1}\right)^{\frac{-1}{4}}\\= q^{ 1 . (\frac{-1}{4}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
10. \(\left(x^{-1}\right)^{\frac{-5}{2}}\\= x^{ -1 . (\frac{-5}{2}) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
11. \(\left(a^{\frac{2}{3}}\right)^{\frac{3}{4}}\\= a^{ \frac{2}{3} . \frac{3}{4} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(\left(q^{\frac{2}{3}}\right)^{\frac{5}{4}}\\= q^{ \frac{2}{3} . \frac{5}{4} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)