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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-5}{6} . (\frac{-1}{4}) }= q^{\frac{5}{24}}\\=\sqrt[24]{ q^{5} }\\---------------\)
2. \(\left(x^{\frac{5}{3}}\right)^{\frac{3}{4}}\\= x^{ \frac{5}{3} . \frac{3}{4} }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
3. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-3}{4} . (\frac{-1}{3}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
4. \(\left(x^{\frac{5}{4}}\right)^{\frac{2}{3}}\\= x^{ \frac{5}{4} . \frac{2}{3} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
5. \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)
6. \(\left(a^{\frac{-5}{3}}\right)^{\frac{3}{4}}\\= a^{ \frac{-5}{3} . \frac{3}{4} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
7. \(\left(q^{\frac{1}{6}}\right)^{\frac{-2}{3}}\\= q^{ \frac{1}{6} . (\frac{-2}{3}) }= q^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ q }}=\frac{1}{\sqrt[9]{ q }}. \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q}\\---------------\)
8. \(\left(x^{\frac{-3}{5}}\right)^{\frac{2}{5}}\\= x^{ \frac{-3}{5} . \frac{2}{5} }= x^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ x^{6} }}=\frac{1}{\sqrt[25]{ x^{6} }}. \color{purple}{\frac{\sqrt[25]{ x^{19} }}{\sqrt[25]{ x^{19} }}} \\=\frac{\sqrt[25]{ x^{19} }}{x}\\---------------\)
9. \(\left(x^{\frac{2}{5}}\right)^{\frac{2}{5}}\\= x^{ \frac{2}{5} . \frac{2}{5} }= x^{\frac{4}{25}}\\=\sqrt[25]{ x^{4} }\\---------------\)
10. \(\left(a^{\frac{3}{2}}\right)^{\frac{-3}{5}}\\= a^{ \frac{3}{2} . (\frac{-3}{5}) }= a^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ a^{9} }}=\frac{1}{\sqrt[10]{ a^{9} }}. \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a|}\\---------------\)
11. \(\left(x^{\frac{-3}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{-3}{5} . \frac{2}{3} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
12. \(\left(a^{\frac{5}{3}}\right)^{\frac{4}{3}}\\= a^{ \frac{5}{3} . \frac{4}{3} }= a^{\frac{20}{9}}\\=\sqrt[9]{ a^{20} }=a^{2}.\sqrt[9]{ a^{2} }\\---------------\)