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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-3}{5} . (\frac{-1}{2}) }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
2. \(\left(a^{\frac{1}{4}}\right)^{\frac{-1}{5}}\\= a^{ \frac{1}{4} . (\frac{-1}{5}) }= a^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ a }}=\frac{1}{\sqrt[20]{ a }}. \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a|}\\---------------\)
3. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{6}}\\= y^{ \frac{-1}{2} . (\frac{-1}{6}) }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
4. \(\left(y^{\frac{-5}{3}}\right)^{\frac{1}{3}}\\= y^{ \frac{-5}{3} . \frac{1}{3} }= y^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ y^{5} }}=\frac{1}{\sqrt[9]{ y^{5} }}. \color{purple}{\frac{\sqrt[9]{ y^{4} }}{\sqrt[9]{ y^{4} }}} \\=\frac{\sqrt[9]{ y^{4} }}{y}\\---------------\)
5. \(\left(a^{\frac{2}{5}}\right)^{\frac{1}{2}}\\= a^{ \frac{2}{5} . \frac{1}{2} }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
6. \(\left(a^{1}\right)^{\frac{3}{2}}\\= a^{ 1 . \frac{3}{2} }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
7. \(\left(x^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{3} . \frac{1}{2} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
8. \(\left(x^{\frac{2}{3}}\right)^{\frac{3}{5}}\\= x^{ \frac{2}{3} . \frac{3}{5} }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
9. \(\left(y^{\frac{5}{2}}\right)^{2}\\= y^{ \frac{5}{2} . 2 }= y^{5}\\\\---------------\)
10. \(\left(q^{\frac{-5}{2}}\right)^{1}\\= q^{ \frac{-5}{2} . 1 }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
11. \(\left(x^{\frac{3}{2}}\right)^{\frac{-4}{3}}\\= x^{ \frac{3}{2} . (\frac{-4}{3}) }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
12. \(\left(x^{\frac{2}{3}}\right)^{1}\\= x^{ \frac{2}{3} . 1 }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)