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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-2}{3}}\right)^{1}\\= x^{ \frac{-2}{3} . 1 }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
2. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-3}{4} . (\frac{-1}{6}) }= a^{\frac{1}{8}}\\=\sqrt[8]{ a }\\---------------\)
3. \(\left(a^{-1}\right)^{\frac{-5}{2}}\\= a^{ -1 . (\frac{-5}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
4. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-3}{2}}\\= q^{ \frac{-1}{4} . (\frac{-3}{2}) }= q^{\frac{3}{8}}\\=\sqrt[8]{ q^{3} }\\---------------\)
5. \(\left(q^{\frac{-3}{2}}\right)^{-1}\\= q^{ \frac{-3}{2} . (-1) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
6. \(\left(q^{\frac{1}{5}}\right)^{\frac{2}{3}}\\= q^{ \frac{1}{5} . \frac{2}{3} }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
7. \(\left(q^{\frac{1}{2}}\right)^{\frac{-5}{2}}\\= q^{ \frac{1}{2} . (\frac{-5}{2}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
8. \(\left(y^{\frac{1}{6}}\right)^{-1}\\= y^{ \frac{1}{6} . (-1) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
9. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-1}{6}}\\= y^{ \frac{-2}{5} . (\frac{-1}{6}) }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
10. \(\left(a^{\frac{2}{3}}\right)^{1}\\= a^{ \frac{2}{3} . 1 }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
11. \(\left(y^{\frac{3}{4}}\right)^{\frac{1}{5}}\\= y^{ \frac{3}{4} . \frac{1}{5} }= y^{\frac{3}{20}}\\=\sqrt[20]{ y^{3} }\\---------------\)
12. \(\left(y^{\frac{3}{5}}\right)^{\frac{-3}{5}}\\= y^{ \frac{3}{5} . (\frac{-3}{5}) }= y^{\frac{-9}{25}}\\=\frac{1}{\sqrt[25]{ y^{9} }}=\frac{1}{\sqrt[25]{ y^{9} }}. \color{purple}{\frac{\sqrt[25]{ y^{16} }}{\sqrt[25]{ y^{16} }}} \\=\frac{\sqrt[25]{ y^{16} }}{y}\\---------------\)