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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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