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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{3}{5}}\right)^{\frac{-2}{3}}\\= a^{ \frac{3}{5} . (\frac{-2}{3}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
2. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-1}{4} . (\frac{-2}{3}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
3. \(\left(x^{\frac{2}{3}}\right)^{\frac{-1}{3}}\\= x^{ \frac{2}{3} . (\frac{-1}{3}) }= x^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ x^{2} }}=\frac{1}{\sqrt[9]{ x^{2} }}. \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x}\\---------------\)
4. \(\left(y^{\frac{1}{2}}\right)^{\frac{-3}{5}}\\= y^{ \frac{1}{2} . (\frac{-3}{5}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
5. \(\left(y^{\frac{1}{6}}\right)^{-1}\\= y^{ \frac{1}{6} . (-1) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
6. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{6}}\\= y^{ \frac{-1}{2} . \frac{1}{6} }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
7. \(\left(a^{\frac{1}{5}}\right)^{\frac{3}{2}}\\= a^{ \frac{1}{5} . \frac{3}{2} }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)
8. \(\left(q^{\frac{1}{6}}\right)^{\frac{-5}{3}}\\= q^{ \frac{1}{6} . (\frac{-5}{3}) }= q^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ q^{5} }}=\frac{1}{\sqrt[18]{ q^{5} }}. \color{purple}{\frac{\sqrt[18]{ q^{13} }}{\sqrt[18]{ q^{13} }}} \\=\frac{\sqrt[18]{ q^{13} }}{|q|}\\---------------\)
9. \(\left(a^{\frac{3}{4}}\right)^{\frac{-2}{5}}\\= a^{ \frac{3}{4} . (\frac{-2}{5}) }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
10. \(\left(q^{1}\right)^{\frac{1}{2}}\\= q^{ 1 . \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
11. \(\left(y^{-1}\right)^{\frac{-2}{3}}\\= y^{ -1 . (\frac{-2}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
12. \(\left(a^{\frac{1}{4}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{4} . (\frac{-1}{2}) }= a^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ a }}=\frac{1}{\sqrt[8]{ a }}. \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a|}\\---------------\)