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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{2}}\right)^{-1}\\= x^{ \frac{-1}{2} . (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
2. \(\left(y^{\frac{-5}{6}}\right)^{\frac{-4}{3}}\\= y^{ \frac{-5}{6} . (\frac{-4}{3}) }= y^{\frac{10}{9}}\\=\sqrt[9]{ y^{10} }=y.\sqrt[9]{ y }\\---------------\)
3. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-1}{4} . (\frac{-1}{4}) }= x^{\frac{1}{16}}\\=\sqrt[16]{ x }\\---------------\)
4. \(\left(a^{\frac{-5}{6}}\right)^{\frac{-1}{5}}\\= a^{ \frac{-5}{6} . (\frac{-1}{5}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
5. \(\left(a^{1}\right)^{\frac{-5}{4}}\\= a^{ 1 . (\frac{-5}{4}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
6. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{2} . (\frac{-1}{2}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
7. \(\left(x^{\frac{2}{3}}\right)^{\frac{5}{4}}\\= x^{ \frac{2}{3} . \frac{5}{4} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
8. \(\left(a^{\frac{4}{5}}\right)^{\frac{1}{5}}\\= a^{ \frac{4}{5} . \frac{1}{5} }= a^{\frac{4}{25}}\\=\sqrt[25]{ a^{4} }\\---------------\)
9. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{5}}\\= y^{ \frac{-1}{2} . \frac{1}{5} }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
10. \(\left(x^{-2}\right)^{\frac{-3}{5}}\\= x^{ -2 . (\frac{-3}{5}) }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
11. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-4}{5} . (\frac{-1}{3}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
12. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-4}{5} . (\frac{-1}{2}) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)