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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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