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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{4}}\right)^{\frac{-5}{4}}\\= q^{ \frac{1}{4} . (\frac{-5}{4}) }= q^{\frac{-5}{16}}\\=\frac{1}{\sqrt[16]{ q^{5} }}=\frac{1}{\sqrt[16]{ q^{5} }}. \color{purple}{\frac{\sqrt[16]{ q^{11} }}{\sqrt[16]{ q^{11} }}} \\=\frac{\sqrt[16]{ q^{11} }}{|q|}\\---------------\)
2. \(\left(q^{\frac{-4}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{-4}{5} . \frac{1}{3} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
3. \(\left(q^{\frac{-4}{5}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-4}{5} . (\frac{-2}{3}) }= q^{\frac{8}{15}}\\=\sqrt[15]{ q^{8} }\\---------------\)
4. \(\left(x^{1}\right)^{\frac{-5}{2}}\\= x^{ 1 . (\frac{-5}{2}) }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
5. \(\left(a^{-1}\right)^{\frac{5}{4}}\\= a^{ -1 . \frac{5}{4} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
6. \(\left(q^{-1}\right)^{\frac{1}{5}}\\= q^{ -1 . \frac{1}{5} }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
7. \(\left(q^{\frac{-5}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{-5}{2} . \frac{1}{2} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
8. \(\left(q^{\frac{-4}{3}}\right)^{\frac{5}{3}}\\= q^{ \frac{-4}{3} . \frac{5}{3} }= q^{\frac{-20}{9}}\\=\frac{1}{\sqrt[9]{ q^{20} }}\\=\frac{1}{q^{2}.\sqrt[9]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[9]{ q^{2} }} \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q^{3}}\\---------------\)
9. \(\left(q^{\frac{-3}{5}}\right)^{\frac{5}{3}}\\= q^{ \frac{-3}{5} . \frac{5}{3} }= q^{-1}\\=\frac{1}{q}\\---------------\)
10. \(\left(y^{\frac{2}{3}}\right)^{\frac{1}{3}}\\= y^{ \frac{2}{3} . \frac{1}{3} }= y^{\frac{2}{9}}\\=\sqrt[9]{ y^{2} }\\---------------\)
11. \(\left(a^{\frac{2}{5}}\right)^{2}\\= a^{ \frac{2}{5} . 2 }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
12. \(\left(a^{\frac{5}{2}}\right)^{\frac{-5}{4}}\\= a^{ \frac{5}{2} . (\frac{-5}{4}) }= a^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ a^{25} }}\\=\frac{1}{|a^{3}|.\sqrt[8]{ a }}=\frac{1}{|a^{3}|.\sqrt[8]{ a }} \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a^{4}|}\\---------------\)