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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{2}}\right)^{1}\\= q^{ \frac{-1}{2} . 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
2. \(\left(a^{\frac{-3}{4}}\right)^{\frac{2}{3}}\\= a^{ \frac{-3}{4} . \frac{2}{3} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
3. \(\left(x^{-2}\right)^{\frac{-1}{2}}\\= x^{ -2 . (\frac{-1}{2}) }= x^{1}\\\\---------------\)
4. \(\left(y^{\frac{-1}{6}}\right)^{\frac{1}{3}}\\= y^{ \frac{-1}{6} . \frac{1}{3} }= y^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ y }}=\frac{1}{\sqrt[18]{ y }}. \color{purple}{\frac{\sqrt[18]{ y^{17} }}{\sqrt[18]{ y^{17} }}} \\=\frac{\sqrt[18]{ y^{17} }}{|y|}\\---------------\)
5. \(\left(a^{\frac{-2}{3}}\right)^{\frac{1}{4}}\\= a^{ \frac{-2}{3} . \frac{1}{4} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
6. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{4}}\\= y^{ \frac{1}{2} . \frac{1}{4} }= y^{\frac{1}{8}}\\=\sqrt[8]{ y }\\---------------\)
7. \(\left(x^{\frac{-2}{3}}\right)^{\frac{4}{3}}\\= x^{ \frac{-2}{3} . \frac{4}{3} }= x^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ x^{8} }}=\frac{1}{\sqrt[9]{ x^{8} }}. \color{purple}{\frac{\sqrt[9]{ x }}{\sqrt[9]{ x }}} \\=\frac{\sqrt[9]{ x }}{x}\\---------------\)
8. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-2}{3} . (\frac{-5}{6}) }= x^{\frac{5}{9}}\\=\sqrt[9]{ x^{5} }\\---------------\)
9. \(\left(y^{1}\right)^{2}\\= y^{ 1 . 2 }= y^{2}\\\\---------------\)
10. \(\left(y^{1}\right)^{\frac{-3}{5}}\\= y^{ 1 . (\frac{-3}{5}) }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
11. \(\left(q^{\frac{-4}{5}}\right)^{-2}\\= q^{ \frac{-4}{5} . (-2) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
12. \(\left(a^{\frac{-1}{6}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{6} . \frac{2}{3} }= a^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ a }}=\frac{1}{\sqrt[9]{ a }}. \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a}\\---------------\)