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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{4}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{4}{3} . \frac{1}{2} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
2. \(\left(q^{1}\right)^{\frac{-2}{3}}\\= q^{ 1 . (\frac{-2}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
3. \(\left(x^{-2}\right)^{\frac{-3}{4}}\\= x^{ -2 . (\frac{-3}{4}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
4. \(\left(a^{\frac{5}{4}}\right)^{\frac{-1}{3}}\\= a^{ \frac{5}{4} . (\frac{-1}{3}) }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
5. \(\left(q^{\frac{-3}{5}}\right)^{1}\\= q^{ \frac{-3}{5} . 1 }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
6. \(\left(x^{\frac{1}{4}}\right)^{-2}\\= x^{ \frac{1}{4} . (-2) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
7. \(\left(a^{-2}\right)^{\frac{1}{4}}\\= a^{ -2 . \frac{1}{4} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
8. \(\left(y^{\frac{1}{3}}\right)^{\frac{-3}{2}}\\= y^{ \frac{1}{3} . (\frac{-3}{2}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
9. \(\left(q^{\frac{1}{6}}\right)^{\frac{5}{6}}\\= q^{ \frac{1}{6} . \frac{5}{6} }= q^{\frac{5}{36}}\\=\sqrt[36]{ q^{5} }\\---------------\)
10. \(\left(y^{-1}\right)^{2}\\= y^{ -1 . 2 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
11. \(\left(a^{\frac{1}{6}}\right)^{2}\\= a^{ \frac{1}{6} . 2 }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
12. \(\left(a^{\frac{-1}{3}}\right)^{-2}\\= a^{ \frac{-1}{3} . (-2) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)