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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{3}{2}}\right)^{\frac{3}{4}}\\= y^{ \frac{3}{2} . \frac{3}{4} }= y^{\frac{9}{8}}\\=\sqrt[8]{ y^{9} }=|y|.\sqrt[8]{ y }\\---------------\)
2. \(\left(a^{1}\right)^{-1}\\= a^{ 1 . (-1) }= a^{-1}\\=\frac{1}{a}\\---------------\)
3. \(\left(x^{-1}\right)^{\frac{-2}{5}}\\= x^{ -1 . (\frac{-2}{5}) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
4. \(\left(q^{1}\right)^{\frac{-1}{4}}\\= q^{ 1 . (\frac{-1}{4}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
5. \(\left(a^{-1}\right)^{-1}\\= a^{ -1 . (-1) }= a^{1}\\\\---------------\)
6. \(\left(x^{\frac{5}{4}}\right)^{\frac{1}{4}}\\= x^{ \frac{5}{4} . \frac{1}{4} }= x^{\frac{5}{16}}\\=\sqrt[16]{ x^{5} }\\---------------\)
7. \(\left(a^{\frac{-1}{3}}\right)^{\frac{1}{4}}\\= a^{ \frac{-1}{3} . \frac{1}{4} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
8. \(\left(y^{\frac{4}{3}}\right)^{\frac{-3}{2}}\\= y^{ \frac{4}{3} . (\frac{-3}{2}) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
9. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-1}{5}}\\= a^{ \frac{-3}{4} . (\frac{-1}{5}) }= a^{\frac{3}{20}}\\=\sqrt[20]{ a^{3} }\\---------------\)
10. \(\left(y^{\frac{1}{3}}\right)^{1}\\= y^{ \frac{1}{3} . 1 }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
11. \(\left(q^{\frac{-1}{6}}\right)^{\frac{5}{3}}\\= q^{ \frac{-1}{6} . \frac{5}{3} }= q^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ q^{5} }}=\frac{1}{\sqrt[18]{ q^{5} }}. \color{purple}{\frac{\sqrt[18]{ q^{13} }}{\sqrt[18]{ q^{13} }}} \\=\frac{\sqrt[18]{ q^{13} }}{|q|}\\---------------\)
12. \(\left(x^{\frac{-5}{4}}\right)^{1}\\= x^{ \frac{-5}{4} . 1 }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)