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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{3}}\right)^{-1}\\= y^{ \frac{-1}{3} . (-1) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
2. \(\left(y^{\frac{-4}{3}}\right)^{-1}\\= y^{ \frac{-4}{3} . (-1) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{\frac{1}{5}}\\= a^{ \frac{-1}{3} . \frac{1}{5} }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
4. \(\left(q^{\frac{1}{3}}\right)^{\frac{5}{2}}\\= q^{ \frac{1}{3} . \frac{5}{2} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
5. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-1}{3} . (\frac{-5}{4}) }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
6. \(\left(q^{\frac{4}{3}}\right)^{\frac{-5}{2}}\\= q^{ \frac{4}{3} . (\frac{-5}{2}) }= q^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ q^{10} }}\\=\frac{1}{q^{3}.\sqrt[3]{ q }}=\frac{1}{q^{3}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{4}}\\---------------\)
7. \(\left(a^{\frac{3}{4}}\right)^{2}\\= a^{ \frac{3}{4} . 2 }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
8. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-2}{3} . (\frac{-1}{2}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
9. \(\left(q^{\frac{-1}{2}}\right)^{\frac{5}{6}}\\= q^{ \frac{-1}{2} . \frac{5}{6} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
10. \(\left(a^{-2}\right)^{\frac{-4}{3}}\\= a^{ -2 . (\frac{-4}{3}) }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
11. \(\left(q^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{2}{3} . (\frac{-1}{2}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
12. \(\left(x^{\frac{5}{4}}\right)^{-2}\\= x^{ \frac{5}{4} . (-2) }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)