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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{2}\right)^{\frac{2}{3}}\\= y^{ 2 . \frac{2}{3} }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
2. \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
3. \(\left(y^{\frac{2}{3}}\right)^{\frac{-5}{4}}\\= y^{ \frac{2}{3} . (\frac{-5}{4}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
4. \(\left(y^{\frac{3}{2}}\right)^{\frac{-4}{3}}\\= y^{ \frac{3}{2} . (\frac{-4}{3}) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
5. \(\left(a^{\frac{1}{2}}\right)^{1}\\= a^{ \frac{1}{2} . 1 }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
6. \(\left(x^{2}\right)^{\frac{-5}{6}}\\= x^{ 2 . (\frac{-5}{6}) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
7. \(\left(a^{\frac{-2}{3}}\right)^{\frac{3}{4}}\\= a^{ \frac{-2}{3} . \frac{3}{4} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
8. \(\left(a^{\frac{-5}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-5}{2} . (\frac{-1}{2}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
9. \(\left(q^{-2}\right)^{\frac{-4}{3}}\\= q^{ -2 . (\frac{-4}{3}) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
10. \(\left(x^{\frac{5}{6}}\right)^{\frac{1}{6}}\\= x^{ \frac{5}{6} . \frac{1}{6} }= x^{\frac{5}{36}}\\=\sqrt[36]{ x^{5} }\\---------------\)
11. \(\left(y^{-1}\right)^{\frac{-1}{4}}\\= y^{ -1 . (\frac{-1}{4}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
12. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-2}{5}}\\= x^{ \frac{-4}{5} . (\frac{-2}{5}) }= x^{\frac{8}{25}}\\=\sqrt[25]{ x^{8} }\\---------------\)