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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-1}{4} . (\frac{-1}{2}) }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)
2. \(\left(x^{\frac{-1}{3}}\right)^{1}\\= x^{ \frac{-1}{3} . 1 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
3. \(\left(a^{\frac{2}{5}}\right)^{\frac{2}{3}}\\= a^{ \frac{2}{5} . \frac{2}{3} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
4. \(\left(x^{-1}\right)^{\frac{-3}{2}}\\= x^{ -1 . (\frac{-3}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
5. \(\left(q^{\frac{-5}{6}}\right)^{\frac{1}{4}}\\= q^{ \frac{-5}{6} . \frac{1}{4} }= q^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ q^{5} }}=\frac{1}{\sqrt[24]{ q^{5} }}. \color{purple}{\frac{\sqrt[24]{ q^{19} }}{\sqrt[24]{ q^{19} }}} \\=\frac{\sqrt[24]{ q^{19} }}{|q|}\\---------------\)
6. \(\left(y^{\frac{-1}{4}}\right)^{\frac{3}{4}}\\= y^{ \frac{-1}{4} . \frac{3}{4} }= y^{\frac{-3}{16}}\\=\frac{1}{\sqrt[16]{ y^{3} }}=\frac{1}{\sqrt[16]{ y^{3} }}. \color{purple}{\frac{\sqrt[16]{ y^{13} }}{\sqrt[16]{ y^{13} }}} \\=\frac{\sqrt[16]{ y^{13} }}{|y|}\\---------------\)
7. \(\left(y^{\frac{2}{3}}\right)^{\frac{-2}{5}}\\= y^{ \frac{2}{3} . (\frac{-2}{5}) }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
8. \(\left(q^{\frac{1}{2}}\right)^{1}\\= q^{ \frac{1}{2} . 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
9. \(\left(x^{\frac{-5}{4}}\right)^{1}\\= x^{ \frac{-5}{4} . 1 }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
10. \(\left(x^{\frac{1}{6}}\right)^{\frac{-1}{2}}\\= x^{ \frac{1}{6} . (\frac{-1}{2}) }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
11. \(\left(x^{\frac{4}{3}}\right)^{1}\\= x^{ \frac{4}{3} . 1 }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
12. \(\left(x^{1}\right)^{\frac{3}{4}}\\= x^{ 1 . \frac{3}{4} }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)