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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
2. \(\left(y^{1}\right)^{\frac{1}{2}}\\= y^{ 1 . \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
3. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-5}{3} . (\frac{-3}{5}) }= a^{1}\\\\---------------\)
4. \(\left(q^{-2}\right)^{\frac{-1}{2}}\\= q^{ -2 . (\frac{-1}{2}) }= q^{1}\\\\---------------\)
5. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-4}{5}}\\= a^{ \frac{-1}{2} . (\frac{-4}{5}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
6. \(\left(q^{\frac{-5}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-5}{3} . (\frac{-1}{2}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
7. \(\left(y^{\frac{3}{5}}\right)^{\frac{-1}{4}}\\= y^{ \frac{3}{5} . (\frac{-1}{4}) }= y^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ y^{3} }}=\frac{1}{\sqrt[20]{ y^{3} }}. \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y|}\\---------------\)
8. \(\left(x^{\frac{2}{3}}\right)^{\frac{-4}{3}}\\= x^{ \frac{2}{3} . (\frac{-4}{3}) }= x^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ x^{8} }}=\frac{1}{\sqrt[9]{ x^{8} }}. \color{purple}{\frac{\sqrt[9]{ x }}{\sqrt[9]{ x }}} \\=\frac{\sqrt[9]{ x }}{x}\\---------------\)
9. \(\left(a^{\frac{2}{3}}\right)^{\frac{-3}{5}}\\= a^{ \frac{2}{3} . (\frac{-3}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
10. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-2}{3} . (\frac{-1}{6}) }= q^{\frac{1}{9}}\\=\sqrt[9]{ q }\\---------------\)
11. \(\left(a^{\frac{-1}{5}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{5} . \frac{2}{3} }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
12. \(\left(x^{\frac{5}{3}}\right)^{\frac{1}{6}}\\= x^{ \frac{5}{3} . \frac{1}{6} }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)