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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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