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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{2}\right)^{\frac{2}{3}}\\= x^{ 2 . \frac{2}{3} }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
2. \(\left(y^{\frac{-5}{6}}\right)^{1}\\= y^{ \frac{-5}{6} . 1 }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
3. \(\left(a^{\frac{3}{4}}\right)^{\frac{1}{6}}\\= a^{ \frac{3}{4} . \frac{1}{6} }= a^{\frac{1}{8}}\\=\sqrt[8]{ a }\\---------------\)
4. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-1}{3} . (\frac{-2}{5}) }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
5. \(\left(x^{\frac{1}{3}}\right)^{\frac{5}{2}}\\= x^{ \frac{1}{3} . \frac{5}{2} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
6. \(\left(a^{\frac{4}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{4}{5} . (\frac{-1}{2}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
7. \(\left(x^{\frac{-4}{5}}\right)^{\frac{4}{3}}\\= x^{ \frac{-4}{5} . \frac{4}{3} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
8. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-1}{5}}\\= x^{ \frac{-1}{3} . (\frac{-1}{5}) }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
9. \(\left(x^{1}\right)^{\frac{1}{6}}\\= x^{ 1 . \frac{1}{6} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{-1}\\= q^{ \frac{1}{2} . (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
11. \(\left(a^{-2}\right)^{\frac{1}{5}}\\= a^{ -2 . \frac{1}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
12. \(\left(x^{\frac{2}{3}}\right)^{\frac{-5}{3}}\\= x^{ \frac{2}{3} . (\frac{-5}{3}) }= x^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ x^{10} }}\\=\frac{1}{x.\sqrt[9]{ x }}=\frac{1}{x.\sqrt[9]{ x }} \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x^{2}}\\---------------\)