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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{4}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{4}{5} . (\frac{-1}{2}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
2. \(\left(y^{\frac{-5}{6}}\right)^{\frac{2}{3}}\\= y^{ \frac{-5}{6} . \frac{2}{3} }= y^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ y^{5} }}=\frac{1}{\sqrt[9]{ y^{5} }}. \color{purple}{\frac{\sqrt[9]{ y^{4} }}{\sqrt[9]{ y^{4} }}} \\=\frac{\sqrt[9]{ y^{4} }}{y}\\---------------\)
3. \(\left(q^{\frac{1}{2}}\right)^{1}\\= q^{ \frac{1}{2} . 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
4. \(\left(a^{\frac{5}{2}}\right)^{-1}\\= a^{ \frac{5}{2} . (-1) }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
5. \(\left(q^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{2} . \frac{1}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
6. \(\left(y^{\frac{-1}{3}}\right)^{\frac{5}{6}}\\= y^{ \frac{-1}{3} . \frac{5}{6} }= y^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ y^{5} }}=\frac{1}{\sqrt[18]{ y^{5} }}. \color{purple}{\frac{\sqrt[18]{ y^{13} }}{\sqrt[18]{ y^{13} }}} \\=\frac{\sqrt[18]{ y^{13} }}{|y|}\\---------------\)
7. \(\left(x^{\frac{-3}{2}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-3}{2} . (\frac{-1}{2}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
8. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-4}{3} . (\frac{-3}{5}) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
9. \(\left(q^{\frac{1}{2}}\right)^{2}\\= q^{ \frac{1}{2} . 2 }= q^{1}\\\\---------------\)
10. \(\left(a^{\frac{1}{3}}\right)^{\frac{-5}{2}}\\= a^{ \frac{1}{3} . (\frac{-5}{2}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
11. \(\left(y^{1}\right)^{\frac{5}{4}}\\= y^{ 1 . \frac{5}{4} }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
12. \(\left(y^{\frac{-2}{5}}\right)^{1}\\= y^{ \frac{-2}{5} . 1 }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)