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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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