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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-3}{5}}\right)^{\frac{5}{4}}\\= x^{ \frac{-3}{5} . \frac{5}{4} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
2. \(\left(a^{\frac{2}{3}}\right)^{2}\\= a^{ \frac{2}{3} . 2 }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
3. \(\left(a^{\frac{1}{6}}\right)^{\frac{1}{6}}\\= a^{ \frac{1}{6} . \frac{1}{6} }= a^{\frac{1}{36}}\\=\sqrt[36]{ a }\\---------------\)
4. \(\left(x^{\frac{4}{5}}\right)^{\frac{3}{5}}\\= x^{ \frac{4}{5} . \frac{3}{5} }= x^{\frac{12}{25}}\\=\sqrt[25]{ x^{12} }\\---------------\)
5. \(\left(q^{1}\right)^{\frac{2}{3}}\\= q^{ 1 . \frac{2}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
6. \(\left(q^{\frac{1}{6}}\right)^{\frac{5}{6}}\\= q^{ \frac{1}{6} . \frac{5}{6} }= q^{\frac{5}{36}}\\=\sqrt[36]{ q^{5} }\\---------------\)
7. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{5}}\\= q^{ \frac{1}{2} . \frac{1}{5} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
8. \(\left(a^{-1}\right)^{\frac{3}{2}}\\= a^{ -1 . \frac{3}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
9. \(\left(a^{2}\right)^{\frac{-3}{2}}\\= a^{ 2 . (\frac{-3}{2}) }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
10. \(\left(a^{\frac{4}{3}}\right)^{-1}\\= a^{ \frac{4}{3} . (-1) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
11. \(\left(q^{\frac{3}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{3}{2} . \frac{1}{2} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
12. \(\left(y^{\frac{-5}{3}}\right)^{\frac{-1}{5}}\\= y^{ \frac{-5}{3} . (\frac{-1}{5}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)