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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{2}}\right)^{\frac{2}{3}}\\= a^{ \frac{5}{2} . \frac{2}{3} }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
2. \(\left(x^{\frac{-5}{4}}\right)^{\frac{-1}{6}}\\= x^{ \frac{-5}{4} . (\frac{-1}{6}) }= x^{\frac{5}{24}}\\=\sqrt[24]{ x^{5} }\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{3} . \frac{2}{3} }= a^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ a^{2} }}=\frac{1}{\sqrt[9]{ a^{2} }}. \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a}\\---------------\)
4. \(\left(q^{\frac{-1}{3}}\right)^{\frac{5}{6}}\\= q^{ \frac{-1}{3} . \frac{5}{6} }= q^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ q^{5} }}=\frac{1}{\sqrt[18]{ q^{5} }}. \color{purple}{\frac{\sqrt[18]{ q^{13} }}{\sqrt[18]{ q^{13} }}} \\=\frac{\sqrt[18]{ q^{13} }}{|q|}\\---------------\)
5. \(\left(a^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{2} . \frac{1}{2} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
6. \(\left(q^{-1}\right)^{\frac{1}{2}}\\= q^{ -1 . \frac{1}{2} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
7. \(\left(a^{1}\right)^{1}\\= a^{ 1 . 1 }= a^{1}\\\\---------------\)
8. \(\left(a^{\frac{-1}{3}}\right)^{\frac{3}{4}}\\= a^{ \frac{-1}{3} . \frac{3}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
9. \(\left(y^{-1}\right)^{2}\\= y^{ -1 . 2 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
10. \(\left(a^{\frac{1}{2}}\right)^{1}\\= a^{ \frac{1}{2} . 1 }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
11. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-5}{3}}\\= x^{ \frac{-1}{3} . (\frac{-5}{3}) }= x^{\frac{5}{9}}\\=\sqrt[9]{ x^{5} }\\---------------\)
12. \(\left(a^{2}\right)^{\frac{-5}{4}}\\= a^{ 2 . (\frac{-5}{4}) }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)