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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-4}{3}}\right)^{\frac{4}{3}}\\= y^{ \frac{-4}{3} . \frac{4}{3} }= y^{\frac{-16}{9}}\\=\frac{1}{\sqrt[9]{ y^{16} }}\\=\frac{1}{y.\sqrt[9]{ y^{7} }}=\frac{1}{y.\sqrt[9]{ y^{7} }} \color{purple}{\frac{\sqrt[9]{ y^{2} }}{\sqrt[9]{ y^{2} }}} \\=\frac{\sqrt[9]{ y^{2} }}{y^{2}}\\---------------\)
2. \(\left(q^{1}\right)^{-1}\\= q^{ 1 . (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
3. \(\left(x^{\frac{-3}{4}}\right)^{\frac{3}{5}}\\= x^{ \frac{-3}{4} . \frac{3}{5} }= x^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ x^{9} }}=\frac{1}{\sqrt[20]{ x^{9} }}. \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x|}\\---------------\)
4. \(\left(a^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{2} . \frac{1}{2} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
5. \(\left(a^{\frac{3}{2}}\right)^{\frac{5}{4}}\\= a^{ \frac{3}{2} . \frac{5}{4} }= a^{\frac{15}{8}}\\=\sqrt[8]{ a^{15} }=|a|.\sqrt[8]{ a^{7} }\\---------------\)
6. \(\left(x^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= x^{ \frac{1}{2} . \frac{1}{3} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
7. \(\left(a^{\frac{1}{2}}\right)^{-2}\\= a^{ \frac{1}{2} . (-2) }= a^{-1}\\=\frac{1}{a}\\---------------\)
8. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-1}{4} . (\frac{-5}{4}) }= x^{\frac{5}{16}}\\=\sqrt[16]{ x^{5} }\\---------------\)
9. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-5}{6} . (\frac{-5}{4}) }= x^{\frac{25}{24}}\\=\sqrt[24]{ x^{25} }=|x|.\sqrt[24]{ x }\\---------------\)
10. \(\left(q^{\frac{2}{3}}\right)^{\frac{2}{3}}\\= q^{ \frac{2}{3} . \frac{2}{3} }= q^{\frac{4}{9}}\\=\sqrt[9]{ q^{4} }\\---------------\)
11. \(\left(y^{\frac{-5}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-5}{2} . (\frac{-1}{2}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
12. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-1}{3} . (\frac{-5}{6}) }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)