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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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