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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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