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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{2} . \frac{1}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
2. \(\left(q^{\frac{5}{3}}\right)^{\frac{-5}{6}}\\= q^{ \frac{5}{3} . (\frac{-5}{6}) }= q^{\frac{-25}{18}}\\=\frac{1}{\sqrt[18]{ q^{25} }}\\=\frac{1}{|q|.\sqrt[18]{ q^{7} }}=\frac{1}{|q|.\sqrt[18]{ q^{7} }} \color{purple}{\frac{\sqrt[18]{ q^{11} }}{\sqrt[18]{ q^{11} }}} \\=\frac{\sqrt[18]{ q^{11} }}{|q^{2}|}\\---------------\)
3. \(\left(x^{1}\right)^{1}\\= x^{ 1 . 1 }= x^{1}\\\\---------------\)
4. \(\left(x^{\frac{1}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{1}{3} . (\frac{-2}{3}) }= x^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ x^{2} }}=\frac{1}{\sqrt[9]{ x^{2} }}. \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x}\\---------------\)
5. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-3}{2}}\\= q^{ \frac{-1}{2} . (\frac{-3}{2}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
6. \(\left(a^{\frac{-1}{5}}\right)^{2}\\= a^{ \frac{-1}{5} . 2 }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{-5}{3}}\\= a^{ -1 . (\frac{-5}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
8. \(\left(a^{\frac{1}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{5} . (\frac{-1}{2}) }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
9. \(\left(x^{\frac{1}{2}}\right)^{-1}\\= x^{ \frac{1}{2} . (-1) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
10. \(\left(y^{\frac{5}{3}}\right)^{1}\\= y^{ \frac{5}{3} . 1 }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
11. \(\left(x^{-2}\right)^{\frac{5}{2}}\\= x^{ -2 . \frac{5}{2} }= x^{-5}\\=\frac{1}{x^{5}}\\---------------\)
12. \(\left(y^{-1}\right)^{\frac{3}{5}}\\= y^{ -1 . \frac{3}{5} }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)