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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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