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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{5}{6}}\right)^{-1}\\= y^{ \frac{5}{6} . (-1) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
2. \(\left(x^{\frac{1}{2}}\right)^{\frac{2}{3}}\\= x^{ \frac{1}{2} . \frac{2}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
3. \(\left(a^{\frac{5}{4}}\right)^{-1}\\= a^{ \frac{5}{4} . (-1) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
4. \(\left(x^{-2}\right)^{\frac{-3}{2}}\\= x^{ -2 . (\frac{-3}{2}) }= x^{3}\\\\---------------\)
5. \(\left(a^{\frac{-1}{3}}\right)^{\frac{1}{6}}\\= a^{ \frac{-1}{3} . \frac{1}{6} }= a^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ a }}=\frac{1}{\sqrt[18]{ a }}. \color{purple}{\frac{\sqrt[18]{ a^{17} }}{\sqrt[18]{ a^{17} }}} \\=\frac{\sqrt[18]{ a^{17} }}{|a|}\\---------------\)
6. \(\left(x^{-1}\right)^{\frac{2}{3}}\\= x^{ -1 . \frac{2}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
7. \(\left(x^{\frac{-3}{2}}\right)^{\frac{2}{5}}\\= x^{ \frac{-3}{2} . \frac{2}{5} }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
8. \(\left(y^{\frac{2}{5}}\right)^{\frac{-2}{5}}\\= y^{ \frac{2}{5} . (\frac{-2}{5}) }= y^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ y^{4} }}=\frac{1}{\sqrt[25]{ y^{4} }}. \color{purple}{\frac{\sqrt[25]{ y^{21} }}{\sqrt[25]{ y^{21} }}} \\=\frac{\sqrt[25]{ y^{21} }}{y}\\---------------\)
9. \(\left(q^{\frac{1}{4}}\right)^{\frac{-1}{2}}\\= q^{ \frac{1}{4} . (\frac{-1}{2}) }= q^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ q }}=\frac{1}{\sqrt[8]{ q }}. \color{purple}{\frac{\sqrt[8]{ q^{7} }}{\sqrt[8]{ q^{7} }}} \\=\frac{\sqrt[8]{ q^{7} }}{|q|}\\---------------\)
10. \(\left(a^{\frac{2}{3}}\right)^{\frac{4}{5}}\\= a^{ \frac{2}{3} . \frac{4}{5} }= a^{\frac{8}{15}}\\=\sqrt[15]{ a^{8} }\\---------------\)
11. \(\left(q^{1}\right)^{\frac{-2}{3}}\\= q^{ 1 . (\frac{-2}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
12. \(\left(a^{\frac{-2}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{-2}{3} . \frac{1}{3} }= a^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ a^{2} }}=\frac{1}{\sqrt[9]{ a^{2} }}. \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a}\\---------------\)