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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{2}{5}}\right)^{\frac{-1}{3}}\\= y^{ \frac{2}{5} . (\frac{-1}{3}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
2. \(\left(x^{\frac{1}{3}}\right)^{\frac{-3}{4}}\\= x^{ \frac{1}{3} . (\frac{-3}{4}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{-1}{3} . \frac{1}{3} }= a^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ a }}=\frac{1}{\sqrt[9]{ a }}. \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a}\\---------------\)
4. \(\left(q^{-1}\right)^{\frac{3}{2}}\\= q^{ -1 . \frac{3}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
5. \(\left(x^{\frac{-3}{4}}\right)^{\frac{3}{4}}\\= x^{ \frac{-3}{4} . \frac{3}{4} }= x^{\frac{-9}{16}}\\=\frac{1}{\sqrt[16]{ x^{9} }}=\frac{1}{\sqrt[16]{ x^{9} }}. \color{purple}{\frac{\sqrt[16]{ x^{7} }}{\sqrt[16]{ x^{7} }}} \\=\frac{\sqrt[16]{ x^{7} }}{|x|}\\---------------\)
6. \(\left(q^{\frac{-1}{4}}\right)^{-1}\\= q^{ \frac{-1}{4} . (-1) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
7. \(\left(q^{1}\right)^{\frac{1}{4}}\\= q^{ 1 . \frac{1}{4} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
8. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{2} . (\frac{-1}{2}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
9. \(\left(y^{\frac{-1}{2}}\right)^{-1}\\= y^{ \frac{-1}{2} . (-1) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
10. \(\left(y^{\frac{-1}{3}}\right)^{-1}\\= y^{ \frac{-1}{3} . (-1) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
11. \(\left(y^{\frac{4}{3}}\right)^{1}\\= y^{ \frac{4}{3} . 1 }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
12. \(\left(a^{\frac{5}{6}}\right)^{\frac{-1}{2}}\\= a^{ \frac{5}{6} . (\frac{-1}{2}) }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)