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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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