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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{2} . \frac{1}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
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. \(\left(y^{\frac{-3}{5}}\right)^{\frac{1}{2}}\\= y^{ \frac{-3}{5} . \frac{1}{2} }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
4. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-3}{2}}\\= q^{ \frac{-1}{2} . (\frac{-3}{2}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
5. \(\left(y^{\frac{1}{3}}\right)^{\frac{1}{5}}\\= y^{ \frac{1}{3} . \frac{1}{5} }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
6. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-4}{5}}\\= q^{ \frac{-2}{5} . (\frac{-4}{5}) }= q^{\frac{8}{25}}\\=\sqrt[25]{ q^{8} }\\---------------\)
7. \(\left(x^{\frac{1}{6}}\right)^{\frac{-5}{2}}\\= x^{ \frac{1}{6} . (\frac{-5}{2}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
8. \(\left(a^{\frac{2}{3}}\right)^{\frac{4}{3}}\\= a^{ \frac{2}{3} . \frac{4}{3} }= a^{\frac{8}{9}}\\=\sqrt[9]{ a^{8} }\\---------------\)
9. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-2}{3} . (\frac{-1}{2}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
10. \(\left(x^{\frac{-4}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{-4}{5} . \frac{1}{2} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
11. \(\left(x^{\frac{-3}{4}}\right)^{\frac{5}{2}}\\= x^{ \frac{-3}{4} . \frac{5}{2} }= x^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ x^{15} }}\\=\frac{1}{|x|.\sqrt[8]{ x^{7} }}=\frac{1}{|x|.\sqrt[8]{ x^{7} }} \color{purple}{\frac{\sqrt[8]{ x }}{\sqrt[8]{ x }}} \\=\frac{\sqrt[8]{ x }}{|x^{2}|}\\---------------\)
12. \(\left(y^{\frac{2}{5}}\right)^{1}\\= y^{ \frac{2}{5} . 1 }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)