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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-2}{3} . (\frac{-2}{3}) }= x^{\frac{4}{9}}\\=\sqrt[9]{ x^{4} }\\---------------\)
2. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-1}{5} . (\frac{-3}{4}) }= y^{\frac{3}{20}}\\=\sqrt[20]{ y^{3} }\\---------------\)
3. \(\left(x^{\frac{-1}{5}}\right)^{\frac{-1}{6}}\\= x^{ \frac{-1}{5} . (\frac{-1}{6}) }= x^{\frac{1}{30}}\\=\sqrt[30]{ x }\\---------------\)
4. \(\left(q^{\frac{2}{3}}\right)^{\frac{-2}{3}}\\= q^{ \frac{2}{3} . (\frac{-2}{3}) }= q^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ q^{4} }}=\frac{1}{\sqrt[9]{ q^{4} }}. \color{purple}{\frac{\sqrt[9]{ q^{5} }}{\sqrt[9]{ q^{5} }}} \\=\frac{\sqrt[9]{ q^{5} }}{q}\\---------------\)
5. \(\left(x^{\frac{-1}{2}}\right)^{\frac{5}{2}}\\= x^{ \frac{-1}{2} . \frac{5}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
6. \(\left(a^{-2}\right)^{\frac{2}{3}}\\= a^{ -2 . \frac{2}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
7. \(\left(x^{\frac{-1}{2}}\right)^{1}\\= x^{ \frac{-1}{2} . 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
8. \(\left(x^{\frac{2}{5}}\right)^{\frac{3}{2}}\\= x^{ \frac{2}{5} . \frac{3}{2} }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
9. \(\left(y^{\frac{3}{2}}\right)^{\frac{3}{5}}\\= y^{ \frac{3}{2} . \frac{3}{5} }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
10. \(\left(q^{\frac{-3}{5}}\right)^{1}\\= q^{ \frac{-3}{5} . 1 }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
11. \(\left(a^{\frac{3}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{3}{2} . \frac{1}{2} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
12. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{3} . (\frac{-1}{2}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)