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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{3} . (\frac{-1}{2}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
2. \(\left(q^{\frac{3}{4}}\right)^{-1}\\= q^{ \frac{3}{4} . (-1) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
3. \(\left(a^{-1}\right)^{\frac{5}{3}}\\= a^{ -1 . \frac{5}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
4. \(\left(y^{-1}\right)^{1}\\= y^{ -1 . 1 }= y^{-1}\\=\frac{1}{y}\\---------------\)
5. \(\left(x^{\frac{1}{4}}\right)^{\frac{1}{4}}\\= x^{ \frac{1}{4} . \frac{1}{4} }= x^{\frac{1}{16}}\\=\sqrt[16]{ x }\\---------------\)
6. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-5}{3} . (\frac{-4}{5}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
7. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-5}{6} . (\frac{-5}{3}) }= q^{\frac{25}{18}}\\=\sqrt[18]{ q^{25} }=|q|.\sqrt[18]{ q^{7} }\\---------------\)
8. \(\left(a^{1}\right)^{-1}\\= a^{ 1 . (-1) }= a^{-1}\\=\frac{1}{a}\\---------------\)
9. \(\left(q^{1}\right)^{\frac{2}{3}}\\= q^{ 1 . \frac{2}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
10. \(\left(x^{\frac{-2}{3}}\right)^{\frac{5}{4}}\\= x^{ \frac{-2}{3} . \frac{5}{4} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
11. \(\left(a^{\frac{1}{2}}\right)^{\frac{-4}{5}}\\= a^{ \frac{1}{2} . (\frac{-4}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
12. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-1}{4} . (\frac{-5}{3}) }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)