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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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