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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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