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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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