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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{1}\right)^{\frac{5}{6}}\\= y^{ 1 . \frac{5}{6} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
2. \(\left(x^{\frac{5}{4}}\right)^{\frac{2}{5}}\\= x^{ \frac{5}{4} . \frac{2}{5} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
3. \(\left(y^{\frac{2}{5}}\right)^{\frac{4}{5}}\\= y^{ \frac{2}{5} . \frac{4}{5} }= y^{\frac{8}{25}}\\=\sqrt[25]{ y^{8} }\\---------------\)
4. \(\left(y^{\frac{-5}{2}}\right)^{1}\\= y^{ \frac{-5}{2} . 1 }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
5. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-1}{3} . (\frac{-3}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
6. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-5}{6}}\\= q^{ \frac{-1}{4} . (\frac{-5}{6}) }= q^{\frac{5}{24}}\\=\sqrt[24]{ q^{5} }\\---------------\)
7. \(\left(a^{1}\right)^{\frac{1}{4}}\\= a^{ 1 . \frac{1}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
8. \(\left(x^{\frac{-4}{5}}\right)^{-1}\\= x^{ \frac{-4}{5} . (-1) }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
9. \(\left(q^{\frac{-5}{2}}\right)^{\frac{3}{4}}\\= q^{ \frac{-5}{2} . \frac{3}{4} }= q^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ q^{15} }}\\=\frac{1}{|q|.\sqrt[8]{ q^{7} }}=\frac{1}{|q|.\sqrt[8]{ q^{7} }} \color{purple}{\frac{\sqrt[8]{ q }}{\sqrt[8]{ q }}} \\=\frac{\sqrt[8]{ q }}{|q^{2}|}\\---------------\)
10. \(\left(q^{\frac{1}{6}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{6} . (\frac{-1}{3}) }= q^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ q }}=\frac{1}{\sqrt[18]{ q }}. \color{purple}{\frac{\sqrt[18]{ q^{17} }}{\sqrt[18]{ q^{17} }}} \\=\frac{\sqrt[18]{ q^{17} }}{|q|}\\---------------\)
11. \(\left(x^{\frac{-5}{4}}\right)^{\frac{5}{2}}\\= x^{ \frac{-5}{4} . \frac{5}{2} }= x^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ x^{25} }}\\=\frac{1}{|x^{3}|.\sqrt[8]{ x }}=\frac{1}{|x^{3}|.\sqrt[8]{ x }} \color{purple}{\frac{\sqrt[8]{ x^{7} }}{\sqrt[8]{ x^{7} }}} \\=\frac{\sqrt[8]{ x^{7} }}{|x^{4}|}\\---------------\)
12. \(\left(x^{\frac{2}{3}}\right)^{2}\\= x^{ \frac{2}{3} . 2 }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)