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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{4}{3}}\right)^{\frac{-5}{3}}\\= y^{ \frac{4}{3} . (\frac{-5}{3}) }= y^{\frac{-20}{9}}\\=\frac{1}{\sqrt[9]{ y^{20} }}\\=\frac{1}{y^{2}.\sqrt[9]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[9]{ y^{2} }} \color{purple}{\frac{\sqrt[9]{ y^{7} }}{\sqrt[9]{ y^{7} }}} \\=\frac{\sqrt[9]{ y^{7} }}{y^{3}}\\---------------\)
2. \(\left(a^{\frac{5}{2}}\right)^{\frac{5}{6}}\\= a^{ \frac{5}{2} . \frac{5}{6} }= a^{\frac{25}{12}}\\=\sqrt[12]{ a^{25} }=|a^{2}|.\sqrt[12]{ a }\\---------------\)
3. \(\left(y^{\frac{-1}{2}}\right)^{\frac{4}{3}}\\= y^{ \frac{-1}{2} . \frac{4}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
4. \(\left(y^{\frac{5}{6}}\right)^{\frac{1}{2}}\\= y^{ \frac{5}{6} . \frac{1}{2} }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
5. \(\left(x^{\frac{5}{3}}\right)^{\frac{3}{2}}\\= x^{ \frac{5}{3} . \frac{3}{2} }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
6. \(\left(a^{1}\right)^{\frac{-4}{3}}\\= a^{ 1 . (\frac{-4}{3}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
7. \(\left(q^{\frac{-1}{3}}\right)^{\frac{2}{5}}\\= q^{ \frac{-1}{3} . \frac{2}{5} }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
8. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-4}{3} . (\frac{-1}{3}) }= q^{\frac{4}{9}}\\=\sqrt[9]{ q^{4} }\\---------------\)
9. \(\left(y^{\frac{1}{2}}\right)^{\frac{-1}{6}}\\= y^{ \frac{1}{2} . (\frac{-1}{6}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
10. \(\left(y^{\frac{-2}{3}}\right)^{\frac{1}{6}}\\= y^{ \frac{-2}{3} . \frac{1}{6} }= y^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ y }}=\frac{1}{\sqrt[9]{ y }}. \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y}\\---------------\)
11. \(\left(q^{\frac{1}{5}}\right)^{\frac{-1}{5}}\\= q^{ \frac{1}{5} . (\frac{-1}{5}) }= q^{\frac{-1}{25}}\\=\frac{1}{\sqrt[25]{ q }}=\frac{1}{\sqrt[25]{ q }}. \color{purple}{\frac{\sqrt[25]{ q^{24} }}{\sqrt[25]{ q^{24} }}} \\=\frac{\sqrt[25]{ q^{24} }}{q}\\---------------\)
12. \(\left(y^{\frac{3}{5}}\right)^{1}\\= y^{ \frac{3}{5} . 1 }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)