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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-2}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{-2}{5} . \frac{1}{3} }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
2. \(\left(a^{\frac{-3}{2}}\right)^{\frac{1}{4}}\\= a^{ \frac{-3}{2} . \frac{1}{4} }= a^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ a^{3} }}=\frac{1}{\sqrt[8]{ a^{3} }}. \color{purple}{\frac{\sqrt[8]{ a^{5} }}{\sqrt[8]{ a^{5} }}} \\=\frac{\sqrt[8]{ a^{5} }}{|a|}\\---------------\)
3. \(\left(y^{\frac{1}{4}}\right)^{\frac{4}{3}}\\= y^{ \frac{1}{4} . \frac{4}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
4. \(\left(a^{\frac{1}{2}}\right)^{\frac{-3}{2}}\\= a^{ \frac{1}{2} . (\frac{-3}{2}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
5. \(\left(a^{1}\right)^{-1}\\= a^{ 1 . (-1) }= a^{-1}\\=\frac{1}{a}\\---------------\)
6. \(\left(a^{\frac{1}{5}}\right)^{\frac{-5}{4}}\\= a^{ \frac{1}{5} . (\frac{-5}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
7. \(\left(a^{\frac{1}{2}}\right)^{-1}\\= a^{ \frac{1}{2} . (-1) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
8. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{2} . (\frac{-1}{2}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
9. \(\left(y^{\frac{-5}{4}}\right)^{\frac{-1}{4}}\\= y^{ \frac{-5}{4} . (\frac{-1}{4}) }= y^{\frac{5}{16}}\\=\sqrt[16]{ y^{5} }\\---------------\)
10. \(\left(q^{\frac{4}{5}}\right)^{\frac{5}{6}}\\= q^{ \frac{4}{5} . \frac{5}{6} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
11. \(\left(q^{\frac{-4}{3}}\right)^{\frac{4}{3}}\\= q^{ \frac{-4}{3} . \frac{4}{3} }= q^{\frac{-16}{9}}\\=\frac{1}{\sqrt[9]{ q^{16} }}\\=\frac{1}{q.\sqrt[9]{ q^{7} }}=\frac{1}{q.\sqrt[9]{ q^{7} }} \color{purple}{\frac{\sqrt[9]{ q^{2} }}{\sqrt[9]{ q^{2} }}} \\=\frac{\sqrt[9]{ q^{2} }}{q^{2}}\\---------------\)
12. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-2}{3} . (\frac{-2}{3}) }= a^{\frac{4}{9}}\\=\sqrt[9]{ a^{4} }\\---------------\)