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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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