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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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