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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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