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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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