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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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