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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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