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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{3}{2}}\right)^{\frac{-4}{5}}\\= x^{ \frac{3}{2} . (\frac{-4}{5}) }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
2. \(\left(q^{\frac{1}{2}}\right)^{\frac{-3}{5}}\\= q^{ \frac{1}{2} . (\frac{-3}{5}) }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)
3. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-1}{6} . (\frac{-5}{3}) }= q^{\frac{5}{18}}\\=\sqrt[18]{ q^{5} }\\---------------\)
4. \(\left(y^{\frac{2}{5}}\right)^{\frac{-4}{5}}\\= y^{ \frac{2}{5} . (\frac{-4}{5}) }= y^{\frac{-8}{25}}\\=\frac{1}{\sqrt[25]{ y^{8} }}=\frac{1}{\sqrt[25]{ y^{8} }}. \color{purple}{\frac{\sqrt[25]{ y^{17} }}{\sqrt[25]{ y^{17} }}} \\=\frac{\sqrt[25]{ y^{17} }}{y}\\---------------\)
5. \(\left(x^{\frac{-2}{5}}\right)^{\frac{3}{2}}\\= x^{ \frac{-2}{5} . \frac{3}{2} }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
6. \(\left(a^{1}\right)^{\frac{1}{2}}\\= a^{ 1 . \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
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. \(\left(x^{-1}\right)^{\frac{2}{3}}\\= x^{ -1 . \frac{2}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
9. \(\left(q^{\frac{-3}{4}}\right)^{\frac{1}{2}}\\= q^{ \frac{-3}{4} . \frac{1}{2} }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}. \color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)
10. \(\left(y^{\frac{5}{3}}\right)^{\frac{-2}{5}}\\= y^{ \frac{5}{3} . (\frac{-2}{5}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
11. \(\left(x^{\frac{5}{6}}\right)^{\frac{-1}{3}}\\= x^{ \frac{5}{6} . (\frac{-1}{3}) }= x^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ x^{5} }}=\frac{1}{\sqrt[18]{ x^{5} }}. \color{purple}{\frac{\sqrt[18]{ x^{13} }}{\sqrt[18]{ x^{13} }}} \\=\frac{\sqrt[18]{ x^{13} }}{|x|}\\---------------\)
12. \(\left(q^{\frac{3}{2}}\right)^{\frac{-1}{5}}\\= q^{ \frac{3}{2} . (\frac{-1}{5}) }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)