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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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