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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{4}{3}}\right)^{\frac{-3}{4}}\\= a^{ \frac{4}{3} . (\frac{-3}{4}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
2. \(\left(a^{-1}\right)^{1}\\= a^{ -1 . 1 }= a^{-1}\\=\frac{1}{a}\\---------------\)
3. \(\left(x^{-1}\right)^{\frac{-1}{2}}\\= x^{ -1 . (\frac{-1}{2}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
4. \(\left(q^{\frac{-1}{3}}\right)^{\frac{2}{5}}\\= q^{ \frac{-1}{3} . \frac{2}{5} }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
5. \(\left(a^{\frac{5}{6}}\right)^{\frac{-3}{2}}\\= a^{ \frac{5}{6} . (\frac{-3}{2}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
6. \(\left(x^{\frac{-3}{2}}\right)^{1}\\= x^{ \frac{-3}{2} . 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
7. \(\left(a^{\frac{-1}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-1}{5} . (\frac{-3}{5}) }= a^{\frac{3}{25}}\\=\sqrt[25]{ a^{3} }\\---------------\)
8. \(\left(y^{\frac{2}{5}}\right)^{\frac{-5}{3}}\\= y^{ \frac{2}{5} . (\frac{-5}{3}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
9. \(\left(a^{-1}\right)^{-1}\\= a^{ -1 . (-1) }= a^{1}\\\\---------------\)
10. \(\left(a^{\frac{1}{6}}\right)^{\frac{-3}{5}}\\= a^{ \frac{1}{6} . (\frac{-3}{5}) }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
11. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{5}}\\= a^{ \frac{1}{3} . \frac{1}{5} }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)
12. \(\left(a^{\frac{4}{3}}\right)^{\frac{5}{3}}\\= a^{ \frac{4}{3} . \frac{5}{3} }= a^{\frac{20}{9}}\\=\sqrt[9]{ a^{20} }=a^{2}.\sqrt[9]{ a^{2} }\\---------------\)