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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-3}{5}}\\= y^{ \frac{-1}{3} . (\frac{-3}{5}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
2. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-2}{3} . (\frac{-1}{3}) }= y^{\frac{2}{9}}\\=\sqrt[9]{ y^{2} }\\---------------\)
3. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-2}{3} . (\frac{-3}{4}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
4. \(\left(x^{\frac{-1}{2}}\right)^{1}\\= x^{ \frac{-1}{2} . 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
5. \(\left(a^{\frac{4}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{4}{3} . \frac{2}{3} }= a^{\frac{8}{9}}\\=\sqrt[9]{ a^{8} }\\---------------\)
6. \(\left(x^{-1}\right)^{\frac{2}{5}}\\= x^{ -1 . \frac{2}{5} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
7. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-1}{3} . (\frac{-5}{2}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
8. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{2} . (\frac{-1}{2}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
9. \(\left(x^{1}\right)^{\frac{-1}{2}}\\= x^{ 1 . (\frac{-1}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
10. \(\left(q^{-1}\right)^{\frac{4}{3}}\\= q^{ -1 . \frac{4}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
11. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-5}{6}}\\= a^{ \frac{-1}{3} . (\frac{-5}{6}) }= a^{\frac{5}{18}}\\=\sqrt[18]{ a^{5} }\\---------------\)
12. \(\left(y^{\frac{2}{3}}\right)^{\frac{1}{6}}\\= y^{ \frac{2}{3} . \frac{1}{6} }= y^{\frac{1}{9}}\\=\sqrt[9]{ y }\\---------------\)