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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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