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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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