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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-5}{6}}\right)^{\frac{-3}{2}}\\= y^{ \frac{-5}{6} . (\frac{-3}{2}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
2. \(\left(a^{\frac{-1}{3}}\right)^{-2}\\= a^{ \frac{-1}{3} . (-2) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
3. \(\left(q^{1}\right)^{\frac{-1}{6}}\\= q^{ 1 . (\frac{-1}{6}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
4. \(\left(q^{\frac{3}{4}}\right)^{\frac{-5}{4}}\\= q^{ \frac{3}{4} . (\frac{-5}{4}) }= q^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ q^{15} }}=\frac{1}{\sqrt[16]{ q^{15} }}. \color{purple}{\frac{\sqrt[16]{ q }}{\sqrt[16]{ q }}} \\=\frac{\sqrt[16]{ q }}{|q|}\\---------------\)
5. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-1}{6}}\\= y^{ \frac{-4}{5} . (\frac{-1}{6}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
6. \(\left(q^{\frac{5}{2}}\right)^{\frac{2}{5}}\\= q^{ \frac{5}{2} . \frac{2}{5} }= q^{1}\\\\---------------\)
7. \(\left(y^{\frac{1}{2}}\right)^{\frac{-4}{5}}\\= y^{ \frac{1}{2} . (\frac{-4}{5}) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
8. \(\left(q^{1}\right)^{\frac{-1}{4}}\\= q^{ 1 . (\frac{-1}{4}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
9. \(\left(a^{\frac{1}{6}}\right)^{-1}\\= a^{ \frac{1}{6} . (-1) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
10. \(\left(a^{\frac{3}{5}}\right)^{\frac{-2}{3}}\\= a^{ \frac{3}{5} . (\frac{-2}{3}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
11. \(\left(y^{\frac{1}{3}}\right)^{\frac{5}{4}}\\= y^{ \frac{1}{3} . \frac{5}{4} }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
12. \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)