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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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