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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= x^{ \frac{-1}{2} . \frac{1}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
2. \(\left(a^{\frac{3}{2}}\right)^{\frac{-4}{3}}\\= a^{ \frac{3}{2} . (\frac{-4}{3}) }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
3. \(\left(x^{2}\right)^{\frac{-2}{5}}\\= x^{ 2 . (\frac{-2}{5}) }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
4. \(\left(a^{\frac{-5}{6}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-5}{6} . (\frac{-1}{6}) }= a^{\frac{5}{36}}\\=\sqrt[36]{ a^{5} }\\---------------\)
5. \(\left(a^{\frac{1}{4}}\right)^{\frac{-2}{3}}\\= a^{ \frac{1}{4} . (\frac{-2}{3}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
6. \(\left(a^{\frac{1}{2}}\right)^{1}\\= a^{ \frac{1}{2} . 1 }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
7. \(\left(y^{1}\right)^{\frac{-5}{3}}\\= y^{ 1 . (\frac{-5}{3}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
8. \(\left(x^{\frac{1}{2}}\right)^{\frac{2}{5}}\\= x^{ \frac{1}{2} . \frac{2}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
9. \(\left(x^{\frac{-2}{3}}\right)^{\frac{4}{3}}\\= x^{ \frac{-2}{3} . \frac{4}{3} }= x^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ x^{8} }}=\frac{1}{\sqrt[9]{ x^{8} }}. \color{purple}{\frac{\sqrt[9]{ x }}{\sqrt[9]{ x }}} \\=\frac{\sqrt[9]{ x }}{x}\\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{6}}\\= q^{ \frac{1}{2} . \frac{1}{6} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
11. \(\left(x^{\frac{5}{4}}\right)^{\frac{3}{4}}\\= x^{ \frac{5}{4} . \frac{3}{4} }= x^{\frac{15}{16}}\\=\sqrt[16]{ x^{15} }\\---------------\)
12. \(\left(a^{1}\right)^{\frac{2}{3}}\\= a^{ 1 . \frac{2}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)