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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-1}\right)^{\frac{-4}{3}}\\= q^{ -1 . (\frac{-4}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
2. \(\left(a^{-1}\right)^{\frac{-5}{2}}\\= a^{ -1 . (\frac{-5}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
3. \(\left(q^{\frac{1}{4}}\right)^{\frac{5}{2}}\\= q^{ \frac{1}{4} . \frac{5}{2} }= q^{\frac{5}{8}}\\=\sqrt[8]{ q^{5} }\\---------------\)
4. \(\left(a^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{2}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
5. \(\left(q^{\frac{4}{5}}\right)^{\frac{-5}{3}}\\= q^{ \frac{4}{5} . (\frac{-5}{3}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
6. \(\left(a^{\frac{5}{3}}\right)^{\frac{5}{6}}\\= a^{ \frac{5}{3} . \frac{5}{6} }= a^{\frac{25}{18}}\\=\sqrt[18]{ a^{25} }=|a|.\sqrt[18]{ a^{7} }\\---------------\)
7. \(\left(a^{\frac{4}{3}}\right)^{\frac{5}{3}}\\= a^{ \frac{4}{3} . \frac{5}{3} }= a^{\frac{20}{9}}\\=\sqrt[9]{ a^{20} }=a^{2}.\sqrt[9]{ a^{2} }\\---------------\)
8. \(\left(x^{\frac{-4}{5}}\right)^{\frac{3}{2}}\\= x^{ \frac{-4}{5} . \frac{3}{2} }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
9. \(\left(q^{1}\right)^{\frac{-3}{2}}\\= q^{ 1 . (\frac{-3}{2}) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
10. \(\left(y^{1}\right)^{\frac{-3}{4}}\\= y^{ 1 . (\frac{-3}{4}) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
11. \(\left(x^{-1}\right)^{\frac{1}{2}}\\= x^{ -1 . \frac{1}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
12. \(\left(x^{\frac{1}{5}}\right)^{2}\\= x^{ \frac{1}{5} . 2 }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)