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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{-2}\right)^{\frac{-1}{3}}\\= a^{ -2 . (\frac{-1}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
2. \(\left(a^{\frac{3}{5}}\right)^{\frac{-1}{6}}\\= a^{ \frac{3}{5} . (\frac{-1}{6}) }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
3. \(\left(q^{\frac{3}{2}}\right)^{-1}\\= q^{ \frac{3}{2} . (-1) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
4. \(\left(q^{1}\right)^{\frac{3}{4}}\\= q^{ 1 . \frac{3}{4} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
5. \(\left(x^{\frac{-2}{3}}\right)^{2}\\= x^{ \frac{-2}{3} . 2 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
6. \(\left(q^{\frac{1}{5}}\right)^{\frac{1}{6}}\\= q^{ \frac{1}{5} . \frac{1}{6} }= q^{\frac{1}{30}}\\=\sqrt[30]{ q }\\---------------\)
7. \(\left(y^{\frac{1}{4}}\right)^{-1}\\= y^{ \frac{1}{4} . (-1) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
8. \(\left(x^{\frac{3}{4}}\right)^{\frac{5}{4}}\\= x^{ \frac{3}{4} . \frac{5}{4} }= x^{\frac{15}{16}}\\=\sqrt[16]{ x^{15} }\\---------------\)
9. \(\left(y^{-1}\right)^{\frac{-2}{5}}\\= y^{ -1 . (\frac{-2}{5}) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
10. \(\left(x^{\frac{3}{2}}\right)^{\frac{2}{3}}\\= x^{ \frac{3}{2} . \frac{2}{3} }= x^{1}\\\\---------------\)
11. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{2} . \frac{1}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
12. \(\left(q^{\frac{1}{3}}\right)^{\frac{1}{4}}\\= q^{ \frac{1}{3} . \frac{1}{4} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)