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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{2}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{2}{3} . (\frac{-1}{3}) }= a^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ a^{2} }}=\frac{1}{\sqrt[9]{ a^{2} }}. \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a}\\---------------\)
2. \(\left(a^{\frac{-1}{6}}\right)^{\frac{5}{6}}\\= a^{ \frac{-1}{6} . \frac{5}{6} }= a^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ a^{5} }}=\frac{1}{\sqrt[36]{ a^{5} }}. \color{purple}{\frac{\sqrt[36]{ a^{31} }}{\sqrt[36]{ a^{31} }}} \\=\frac{\sqrt[36]{ a^{31} }}{|a|}\\---------------\)
3. \(\left(y^{\frac{3}{2}}\right)^{\frac{-1}{6}}\\= y^{ \frac{3}{2} . (\frac{-1}{6}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
4. \(\left(x^{\frac{-4}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-4}{3} . \frac{1}{2} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
5. \(\left(q^{\frac{5}{6}}\right)^{\frac{3}{5}}\\= q^{ \frac{5}{6} . \frac{3}{5} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
6. \(\left(a^{-1}\right)^{\frac{2}{5}}\\= a^{ -1 . \frac{2}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
7. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-1}{2} . (\frac{-1}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
8. \(\left(x^{1}\right)^{\frac{1}{2}}\\= x^{ 1 . \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
9. \(\left(a^{\frac{-1}{6}}\right)^{\frac{1}{4}}\\= a^{ \frac{-1}{6} . \frac{1}{4} }= a^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ a }}=\frac{1}{\sqrt[24]{ a }}. \color{purple}{\frac{\sqrt[24]{ a^{23} }}{\sqrt[24]{ a^{23} }}} \\=\frac{\sqrt[24]{ a^{23} }}{|a|}\\---------------\)
10. \(\left(a^{\frac{4}{5}}\right)^{\frac{-2}{3}}\\= a^{ \frac{4}{5} . (\frac{-2}{3}) }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
11. \(\left(q^{\frac{5}{3}}\right)^{\frac{3}{5}}\\= q^{ \frac{5}{3} . \frac{3}{5} }= q^{1}\\\\---------------\)
12. \(\left(q^{\frac{1}{6}}\right)^{\frac{-4}{5}}\\= q^{ \frac{1}{6} . (\frac{-4}{5}) }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)