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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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