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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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