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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{2} . (\frac{-1}{2}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
2. \(\left(a^{\frac{5}{2}}\right)^{\frac{-2}{3}}\\= a^{ \frac{5}{2} . (\frac{-2}{3}) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
3. \(\left(a^{\frac{4}{3}}\right)^{\frac{-5}{3}}\\= a^{ \frac{4}{3} . (\frac{-5}{3}) }= a^{\frac{-20}{9}}\\=\frac{1}{\sqrt[9]{ a^{20} }}\\=\frac{1}{a^{2}.\sqrt[9]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[9]{ a^{2} }} \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a^{3}}\\---------------\)
4. \(\left(a^{\frac{-3}{4}}\right)^{\frac{3}{4}}\\= a^{ \frac{-3}{4} . \frac{3}{4} }= a^{\frac{-9}{16}}\\=\frac{1}{\sqrt[16]{ a^{9} }}=\frac{1}{\sqrt[16]{ a^{9} }}. \color{purple}{\frac{\sqrt[16]{ a^{7} }}{\sqrt[16]{ a^{7} }}} \\=\frac{\sqrt[16]{ a^{7} }}{|a|}\\---------------\)
5. \(\left(x^{\frac{-1}{5}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-1}{5} . (\frac{-1}{3}) }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
6. \(\left(x^{\frac{1}{2}}\right)^{1}\\= x^{ \frac{1}{2} . 1 }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
7. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{6}}\\= a^{ \frac{1}{3} . \frac{1}{6} }= a^{\frac{1}{18}}\\=\sqrt[18]{ a }\\---------------\)
8. \(\left(a^{\frac{-3}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{-3}{2} . \frac{1}{2} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
9. \(\left(a^{\frac{1}{2}}\right)^{\frac{-2}{3}}\\= a^{ \frac{1}{2} . (\frac{-2}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
10. \(\left(a^{\frac{-3}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-3}{5} . (\frac{-1}{2}) }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)
11. \(\left(q^{\frac{3}{5}}\right)^{\frac{4}{3}}\\= q^{ \frac{3}{5} . \frac{4}{3} }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
12. \(\left(y^{-1}\right)^{\frac{-3}{4}}\\= y^{ -1 . (\frac{-3}{4}) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)