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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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