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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{2}}\right)^{-1}\\= a^{ \frac{-1}{2} . (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
2. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{1}{2} . \frac{1}{2} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
3. \(\left(a^{\frac{-2}{3}}\right)^{-2}\\= a^{ \frac{-2}{3} . (-2) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
4. \(\left(a^{\frac{-1}{4}}\right)^{\frac{1}{6}}\\= a^{ \frac{-1}{4} . \frac{1}{6} }= a^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ a }}=\frac{1}{\sqrt[24]{ a }}. \color{purple}{\frac{\sqrt[24]{ a^{23} }}{\sqrt[24]{ a^{23} }}} \\=\frac{\sqrt[24]{ a^{23} }}{|a|}\\---------------\)
5. \(\left(y^{\frac{1}{6}}\right)^{\frac{2}{3}}\\= y^{ \frac{1}{6} . \frac{2}{3} }= y^{\frac{1}{9}}\\=\sqrt[9]{ y }\\---------------\)
6. \(\left(a^{\frac{-3}{5}}\right)^{\frac{1}{4}}\\= a^{ \frac{-3}{5} . \frac{1}{4} }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
7. \(\left(y^{\frac{-2}{3}}\right)^{\frac{1}{3}}\\= y^{ \frac{-2}{3} . \frac{1}{3} }= y^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ y^{2} }}=\frac{1}{\sqrt[9]{ y^{2} }}. \color{purple}{\frac{\sqrt[9]{ y^{7} }}{\sqrt[9]{ y^{7} }}} \\=\frac{\sqrt[9]{ y^{7} }}{y}\\---------------\)
8. \(\left(y^{\frac{3}{4}}\right)^{\frac{-1}{3}}\\= y^{ \frac{3}{4} . (\frac{-1}{3}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
9. \(\left(a^{\frac{-2}{3}}\right)^{1}\\= a^{ \frac{-2}{3} . 1 }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
10. \(\left(y^{\frac{2}{3}}\right)^{\frac{2}{5}}\\= y^{ \frac{2}{3} . \frac{2}{5} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
11. \(\left(a^{\frac{-1}{2}}\right)^{-2}\\= a^{ \frac{-1}{2} . (-2) }= a^{1}\\\\---------------\)
12. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-5}{2}}\\= y^{ \frac{-1}{3} . (\frac{-5}{2}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)