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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{5}}\right)^{-1}\\= y^{ \frac{1}{5} . (-1) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
2. \(\left(q^{\frac{-2}{5}}\right)^{\frac{3}{5}}\\= q^{ \frac{-2}{5} . \frac{3}{5} }= q^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ q^{6} }}=\frac{1}{\sqrt[25]{ q^{6} }}. \color{purple}{\frac{\sqrt[25]{ q^{19} }}{\sqrt[25]{ q^{19} }}} \\=\frac{\sqrt[25]{ q^{19} }}{q}\\---------------\)
3. \(\left(x^{\frac{3}{2}}\right)^{\frac{-5}{6}}\\= x^{ \frac{3}{2} . (\frac{-5}{6}) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
4. \(\left(y^{\frac{-5}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{-5}{3} . \frac{2}{3} }= y^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ y^{10} }}\\=\frac{1}{y.\sqrt[9]{ y }}=\frac{1}{y.\sqrt[9]{ y }} \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y^{2}}\\---------------\)
5. \(\left(x^{\frac{-5}{2}}\right)^{1}\\= x^{ \frac{-5}{2} . 1 }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
6. \(\left(q^{\frac{-5}{3}}\right)^{\frac{5}{3}}\\= q^{ \frac{-5}{3} . \frac{5}{3} }= q^{\frac{-25}{9}}\\=\frac{1}{\sqrt[9]{ q^{25} }}\\=\frac{1}{q^{2}.\sqrt[9]{ q^{7} }}=\frac{1}{q^{2}.\sqrt[9]{ q^{7} }} \color{purple}{\frac{\sqrt[9]{ q^{2} }}{\sqrt[9]{ q^{2} }}} \\=\frac{\sqrt[9]{ q^{2} }}{q^{3}}\\---------------\)
7. \(\left(a^{\frac{5}{3}}\right)^{1}\\= a^{ \frac{5}{3} . 1 }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
8. \(\left(q^{\frac{5}{2}}\right)^{\frac{-5}{4}}\\= q^{ \frac{5}{2} . (\frac{-5}{4}) }= q^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ q^{25} }}\\=\frac{1}{|q^{3}|.\sqrt[8]{ q }}=\frac{1}{|q^{3}|.\sqrt[8]{ q }} \color{purple}{\frac{\sqrt[8]{ q^{7} }}{\sqrt[8]{ q^{7} }}} \\=\frac{\sqrt[8]{ q^{7} }}{|q^{4}|}\\---------------\)
9. \(\left(y^{\frac{3}{4}}\right)^{\frac{5}{6}}\\= y^{ \frac{3}{4} . \frac{5}{6} }= y^{\frac{5}{8}}\\=\sqrt[8]{ y^{5} }\\---------------\)
10. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-3}{5}}\\= x^{ \frac{-1}{3} . (\frac{-3}{5}) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
11. \(\left(y^{\frac{1}{4}}\right)^{\frac{-5}{6}}\\= y^{ \frac{1}{4} . (\frac{-5}{6}) }= y^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ y^{5} }}=\frac{1}{\sqrt[24]{ y^{5} }}. \color{purple}{\frac{\sqrt[24]{ y^{19} }}{\sqrt[24]{ y^{19} }}} \\=\frac{\sqrt[24]{ y^{19} }}{|y|}\\---------------\)
12. \(\left(q^{\frac{-1}{2}}\right)^{1}\\= q^{ \frac{-1}{2} . 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)