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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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