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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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