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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{6}}\right)^{\frac{-2}{3}}\\= x^{ \frac{5}{6} . (\frac{-2}{3}) }= x^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ x^{5} }}=\frac{1}{\sqrt[9]{ x^{5} }}. \color{purple}{\frac{\sqrt[9]{ x^{4} }}{\sqrt[9]{ x^{4} }}} \\=\frac{\sqrt[9]{ x^{4} }}{x}\\---------------\)
2. \(\left(a^{-1}\right)^{\frac{-1}{2}}\\= a^{ -1 . (\frac{-1}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
3. \(\left(x^{\frac{1}{5}}\right)^{\frac{-1}{5}}\\= x^{ \frac{1}{5} . (\frac{-1}{5}) }= x^{\frac{-1}{25}}\\=\frac{1}{\sqrt[25]{ x }}=\frac{1}{\sqrt[25]{ x }}. \color{purple}{\frac{\sqrt[25]{ x^{24} }}{\sqrt[25]{ x^{24} }}} \\=\frac{\sqrt[25]{ x^{24} }}{x}\\---------------\)
4. \(\left(a^{2}\right)^{\frac{-5}{6}}\\= a^{ 2 . (\frac{-5}{6}) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
5. \(\left(a^{\frac{-2}{3}}\right)^{-1}\\= a^{ \frac{-2}{3} . (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
6. \(\left(a^{\frac{5}{3}}\right)^{-1}\\= a^{ \frac{5}{3} . (-1) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{-3}{4}}\\= a^{ -1 . (\frac{-3}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
8. \(\left(a^{\frac{-1}{4}}\right)^{\frac{5}{2}}\\= a^{ \frac{-1}{4} . \frac{5}{2} }= a^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ a^{5} }}=\frac{1}{\sqrt[8]{ a^{5} }}. \color{purple}{\frac{\sqrt[8]{ a^{3} }}{\sqrt[8]{ a^{3} }}} \\=\frac{\sqrt[8]{ a^{3} }}{|a|}\\---------------\)
9. \(\left(a^{1}\right)^{-1}\\= a^{ 1 . (-1) }= a^{-1}\\=\frac{1}{a}\\---------------\)
10. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-5}{3} . (\frac{-4}{5}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
11. \(\left(q^{\frac{3}{2}}\right)^{\frac{-4}{5}}\\= q^{ \frac{3}{2} . (\frac{-4}{5}) }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
12. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-2}{3} . (\frac{-5}{6}) }= x^{\frac{5}{9}}\\=\sqrt[9]{ x^{5} }\\---------------\)