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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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