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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{1}\right)^{-1}\\= y^{ 1 . (-1) }= y^{-1}\\=\frac{1}{y}\\---------------\)
2. \(\left(q^{\frac{-3}{5}}\right)^{\frac{2}{5}}\\= q^{ \frac{-3}{5} . \frac{2}{5} }= q^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ q^{6} }}=\frac{1}{\sqrt[25]{ q^{6} }}. \color{purple}{\frac{\sqrt[25]{ q^{19} }}{\sqrt[25]{ q^{19} }}} \\=\frac{\sqrt[25]{ q^{19} }}{q}\\---------------\)
3. \(\left(q^{\frac{5}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{5}{2} . \frac{1}{3} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
4. \(\left(a^{\frac{-5}{2}}\right)^{\frac{-1}{5}}\\= a^{ \frac{-5}{2} . (\frac{-1}{5}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
5. \(\left(y^{\frac{1}{6}}\right)^{\frac{1}{3}}\\= y^{ \frac{1}{6} . \frac{1}{3} }= y^{\frac{1}{18}}\\=\sqrt[18]{ y }\\---------------\)
6. \(\left(a^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{2}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
7. \(\left(x^{\frac{2}{3}}\right)^{-1}\\= x^{ \frac{2}{3} . (-1) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
8. \(\left(x^{\frac{5}{6}}\right)^{\frac{-3}{4}}\\= x^{ \frac{5}{6} . (\frac{-3}{4}) }= x^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ x^{5} }}=\frac{1}{\sqrt[8]{ x^{5} }}. \color{purple}{\frac{\sqrt[8]{ x^{3} }}{\sqrt[8]{ x^{3} }}} \\=\frac{\sqrt[8]{ x^{3} }}{|x|}\\---------------\)
9. \(\left(x^{\frac{1}{5}}\right)^{\frac{-5}{4}}\\= x^{ \frac{1}{5} . (\frac{-5}{4}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
10. \(\left(y^{\frac{-5}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{-5}{3} . \frac{1}{2} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
11. \(\left(a^{-1}\right)^{\frac{1}{4}}\\= a^{ -1 . \frac{1}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
12. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)