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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{2}}\right)^{\frac{-3}{5}}\\= y^{ \frac{1}{2} . (\frac{-3}{5}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
2. \(\left(x^{\frac{5}{6}}\right)^{\frac{5}{3}}\\= x^{ \frac{5}{6} . \frac{5}{3} }= x^{\frac{25}{18}}\\=\sqrt[18]{ x^{25} }=|x|.\sqrt[18]{ x^{7} }\\---------------\)
3. \(\left(y^{\frac{-4}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{-4}{3} . \frac{2}{3} }= y^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ y^{8} }}=\frac{1}{\sqrt[9]{ y^{8} }}. \color{purple}{\frac{\sqrt[9]{ y }}{\sqrt[9]{ y }}} \\=\frac{\sqrt[9]{ y }}{y}\\---------------\)
4. \(\left(q^{\frac{1}{2}}\right)^{\frac{-2}{3}}\\= q^{ \frac{1}{2} . (\frac{-2}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
5. \(\left(x^{\frac{1}{2}}\right)^{\frac{3}{5}}\\= x^{ \frac{1}{2} . \frac{3}{5} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
6. \(\left(x^{1}\right)^{\frac{-4}{3}}\\= x^{ 1 . (\frac{-4}{3}) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
7. \(\left(y^{\frac{1}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{5} . (\frac{-1}{2}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
8. \(\left(y^{\frac{-5}{6}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-5}{6} . (\frac{-5}{4}) }= y^{\frac{25}{24}}\\=\sqrt[24]{ y^{25} }=|y|.\sqrt[24]{ y }\\---------------\)
9. \(\left(y^{1}\right)^{\frac{1}{2}}\\= y^{ 1 . \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
10. \(\left(x^{\frac{1}{4}}\right)^{\frac{4}{5}}\\= x^{ \frac{1}{4} . \frac{4}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
11. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-1}{2} . (\frac{-5}{4}) }= y^{\frac{5}{8}}\\=\sqrt[8]{ y^{5} }\\---------------\)
12. \(\left(a^{\frac{3}{4}}\right)^{\frac{-1}{2}}\\= a^{ \frac{3}{4} . (\frac{-1}{2}) }= a^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ a^{3} }}=\frac{1}{\sqrt[8]{ a^{3} }}. \color{purple}{\frac{\sqrt[8]{ a^{5} }}{\sqrt[8]{ a^{5} }}} \\=\frac{\sqrt[8]{ a^{5} }}{|a|}\\---------------\)