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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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