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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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