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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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