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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{5}}\right)^{\frac{-5}{4}}\\= a^{ \frac{1}{5} . (\frac{-5}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
2. \(\left(y^{1}\right)^{\frac{5}{2}}\\= y^{ 1 . \frac{5}{2} }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
3. \(\left(a^{\frac{-3}{5}}\right)^{1}\\= a^{ \frac{-3}{5} . 1 }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
4. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-5}{6} . (\frac{-5}{3}) }= q^{\frac{25}{18}}\\=\sqrt[18]{ q^{25} }=|q|.\sqrt[18]{ q^{7} }\\---------------\)
5. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-1}{2} . (\frac{-3}{4}) }= q^{\frac{3}{8}}\\=\sqrt[8]{ q^{3} }\\---------------\)
6. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-1}{6}}\\= x^{ \frac{-1}{3} . (\frac{-1}{6}) }= x^{\frac{1}{18}}\\=\sqrt[18]{ x }\\---------------\)
7. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{4}}\\= q^{ \frac{-1}{3} . \frac{1}{4} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
8. \(\left(q^{\frac{1}{3}}\right)^{\frac{-4}{3}}\\= q^{ \frac{1}{3} . (\frac{-4}{3}) }= q^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ q^{4} }}=\frac{1}{\sqrt[9]{ q^{4} }}. \color{purple}{\frac{\sqrt[9]{ q^{5} }}{\sqrt[9]{ q^{5} }}} \\=\frac{\sqrt[9]{ q^{5} }}{q}\\---------------\)
9. \(\left(x^{\frac{-3}{2}}\right)^{1}\\= x^{ \frac{-3}{2} . 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
10. \(\left(y^{\frac{-3}{5}}\right)^{2}\\= y^{ \frac{-3}{5} . 2 }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
11. \(\left(x^{1}\right)^{\frac{2}{3}}\\= x^{ 1 . \frac{2}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
12. \(\left(x^{\frac{1}{5}}\right)^{\frac{-2}{5}}\\= x^{ \frac{1}{5} . (\frac{-2}{5}) }= x^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ x^{2} }}=\frac{1}{\sqrt[25]{ x^{2} }}. \color{purple}{\frac{\sqrt[25]{ x^{23} }}{\sqrt[25]{ x^{23} }}} \\=\frac{\sqrt[25]{ x^{23} }}{x}\\---------------\)