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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{3}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{3}{2} . \frac{1}{2} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
2. \(\left(x^{\frac{-4}{5}}\right)^{1}\\= x^{ \frac{-4}{5} . 1 }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
3. \(\left(q^{\frac{5}{6}}\right)^{\frac{2}{3}}\\= q^{ \frac{5}{6} . \frac{2}{3} }= q^{\frac{5}{9}}\\=\sqrt[9]{ q^{5} }\\---------------\)
4. \(\left(q^{1}\right)^{-1}\\= q^{ 1 . (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
5. \(\left(x^{\frac{-4}{5}}\right)^{-1}\\= x^{ \frac{-4}{5} . (-1) }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
6. \(\left(q^{\frac{-3}{4}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-3}{4} . (\frac{-2}{5}) }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
7. \(\left(a^{\frac{3}{4}}\right)^{\frac{-3}{5}}\\= a^{ \frac{3}{4} . (\frac{-3}{5}) }= a^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ a^{9} }}=\frac{1}{\sqrt[20]{ a^{9} }}. \color{purple}{\frac{\sqrt[20]{ a^{11} }}{\sqrt[20]{ a^{11} }}} \\=\frac{\sqrt[20]{ a^{11} }}{|a|}\\---------------\)
8. \(\left(q^{\frac{5}{3}}\right)^{\frac{5}{3}}\\= q^{ \frac{5}{3} . \frac{5}{3} }= q^{\frac{25}{9}}\\=\sqrt[9]{ q^{25} }=q^{2}.\sqrt[9]{ q^{7} }\\---------------\)
9. \(\left(x^{\frac{1}{2}}\right)^{\frac{2}{5}}\\= x^{ \frac{1}{2} . \frac{2}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
10. \(\left(x^{\frac{4}{3}}\right)^{-1}\\= x^{ \frac{4}{3} . (-1) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
11. \(\left(q^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{1}{3} . (\frac{-1}{2}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
12. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-5}{2}}\\= y^{ \frac{-2}{3} . (\frac{-5}{2}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)