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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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