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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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