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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{3}{2}}\right)^{\frac{2}{5}}\\= a^{ \frac{3}{2} . \frac{2}{5} }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
2. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{1}{2} . \frac{1}{2} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
3. \(\left(a^{\frac{1}{5}}\right)^{\frac{-2}{3}}\\= a^{ \frac{1}{5} . (\frac{-2}{3}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
4. \(\left(q^{2}\right)^{\frac{5}{2}}\\= q^{ 2 . \frac{5}{2} }= q^{5}\\\\---------------\)
5. \(\left(q^{\frac{5}{2}}\right)^{-1}\\= q^{ \frac{5}{2} . (-1) }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
6. \(\left(y^{\frac{-5}{4}}\right)^{\frac{5}{3}}\\= y^{ \frac{-5}{4} . \frac{5}{3} }= y^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ y^{25} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y }}=\frac{1}{|y^{2}|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{3}|}\\---------------\)
7. \(\left(q^{\frac{-5}{3}}\right)^{\frac{1}{4}}\\= q^{ \frac{-5}{3} . \frac{1}{4} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
8. \(\left(y^{1}\right)^{\frac{5}{2}}\\= y^{ 1 . \frac{5}{2} }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
9. \(\left(q^{\frac{1}{2}}\right)^{1}\\= q^{ \frac{1}{2} . 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
10. \(\left(a^{-1}\right)^{-2}\\= a^{ -1 . (-2) }= a^{2}\\\\---------------\)
11. \(\left(y^{\frac{-5}{4}}\right)^{\frac{5}{6}}\\= y^{ \frac{-5}{4} . \frac{5}{6} }= y^{\frac{-25}{24}}\\=\frac{1}{\sqrt[24]{ y^{25} }}\\=\frac{1}{|y|.\sqrt[24]{ y }}=\frac{1}{|y|.\sqrt[24]{ y }} \color{purple}{\frac{\sqrt[24]{ y^{23} }}{\sqrt[24]{ y^{23} }}} \\=\frac{\sqrt[24]{ y^{23} }}{|y^{2}|}\\---------------\)
12. \(\left(x^{\frac{-5}{3}}\right)^{2}\\= x^{ \frac{-5}{3} . 2 }= x^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ x^{10} }}\\=\frac{1}{x^{3}.\sqrt[3]{ x }}=\frac{1}{x^{3}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{4}}\\---------------\)