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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-5}{4}}\right)^{1}\\= x^{ \frac{-5}{4} . 1 }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
2. \(\left(a^{\frac{3}{5}}\right)^{1}\\= a^{ \frac{3}{5} . 1 }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
3. \(\left(q^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{2}{3} . (\frac{-1}{2}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
4. \(\left(x^{\frac{-1}{2}}\right)^{\frac{4}{3}}\\= x^{ \frac{-1}{2} . \frac{4}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
5. \(\left(a^{\frac{5}{6}}\right)^{\frac{-2}{3}}\\= a^{ \frac{5}{6} . (\frac{-2}{3}) }= a^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ a^{5} }}=\frac{1}{\sqrt[9]{ a^{5} }}. \color{purple}{\frac{\sqrt[9]{ a^{4} }}{\sqrt[9]{ a^{4} }}} \\=\frac{\sqrt[9]{ a^{4} }}{a}\\---------------\)
6. \(\left(x^{\frac{4}{5}}\right)^{\frac{-5}{2}}\\= x^{ \frac{4}{5} . (\frac{-5}{2}) }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
7. \(\left(x^{\frac{-1}{6}}\right)^{\frac{-1}{5}}\\= x^{ \frac{-1}{6} . (\frac{-1}{5}) }= x^{\frac{1}{30}}\\=\sqrt[30]{ x }\\---------------\)
8. \(\left(y^{\frac{-5}{6}}\right)^{\frac{5}{2}}\\= y^{ \frac{-5}{6} . \frac{5}{2} }= y^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ y^{25} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y }}=\frac{1}{|y^{2}|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{3}|}\\---------------\)
9. \(\left(y^{1}\right)^{\frac{-1}{2}}\\= y^{ 1 . (\frac{-1}{2}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
10. \(\left(x^{\frac{4}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{4}{3} . \frac{1}{2} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
11. \(\left(q^{\frac{5}{6}}\right)^{\frac{-1}{4}}\\= q^{ \frac{5}{6} . (\frac{-1}{4}) }= q^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ q^{5} }}=\frac{1}{\sqrt[24]{ q^{5} }}. \color{purple}{\frac{\sqrt[24]{ q^{19} }}{\sqrt[24]{ q^{19} }}} \\=\frac{\sqrt[24]{ q^{19} }}{|q|}\\---------------\)
12. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-1}{2} . (\frac{-5}{3}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)