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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{6}}\right)^{\frac{5}{3}}\\= y^{ \frac{-1}{6} . \frac{5}{3} }= y^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ y^{5} }}=\frac{1}{\sqrt[18]{ y^{5} }}. \color{purple}{\frac{\sqrt[18]{ y^{13} }}{\sqrt[18]{ y^{13} }}} \\=\frac{\sqrt[18]{ y^{13} }}{|y|}\\---------------\)
2. \(\left(q^{\frac{-1}{3}}\right)^{-1}\\= q^{ \frac{-1}{3} . (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
3. \(\left(x^{-1}\right)^{\frac{-2}{3}}\\= x^{ -1 . (\frac{-2}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
4. \(\left(x^{\frac{-2}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-2}{5} . (\frac{-1}{2}) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
5. \(\left(x^{\frac{-5}{6}}\right)^{-1}\\= x^{ \frac{-5}{6} . (-1) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
6. \(\left(x^{\frac{5}{6}}\right)^{-2}\\= x^{ \frac{5}{6} . (-2) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
7. \(\left(q^{\frac{-3}{4}}\right)^{\frac{-3}{5}}\\= q^{ \frac{-3}{4} . (\frac{-3}{5}) }= q^{\frac{9}{20}}\\=\sqrt[20]{ q^{9} }\\---------------\)
8. \(\left(a^{-1}\right)^{\frac{-4}{3}}\\= a^{ -1 . (\frac{-4}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
9. \(\left(a^{1}\right)^{-1}\\= a^{ 1 . (-1) }= a^{-1}\\=\frac{1}{a}\\---------------\)
10. \(\left(q^{\frac{-2}{3}}\right)^{\frac{4}{5}}\\= q^{ \frac{-2}{3} . \frac{4}{5} }= q^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ q^{8} }}=\frac{1}{\sqrt[15]{ q^{8} }}. \color{purple}{\frac{\sqrt[15]{ q^{7} }}{\sqrt[15]{ q^{7} }}} \\=\frac{\sqrt[15]{ q^{7} }}{q}\\---------------\)
11. \(\left(y^{\frac{-4}{5}}\right)^{1}\\= y^{ \frac{-4}{5} . 1 }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
12. \(\left(y^{\frac{1}{6}}\right)^{-1}\\= y^{ \frac{1}{6} . (-1) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)