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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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