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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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