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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{2}}\right)^{1}\\= a^{ \frac{5}{2} . 1 }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
2. \(\left(a^{\frac{1}{2}}\right)^{2}\\= a^{ \frac{1}{2} . 2 }= a^{1}\\\\---------------\)
3. \(\left(y^{\frac{3}{2}}\right)^{\frac{-5}{4}}\\= y^{ \frac{3}{2} . (\frac{-5}{4}) }= y^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ y^{15} }}\\=\frac{1}{|y|.\sqrt[8]{ y^{7} }}=\frac{1}{|y|.\sqrt[8]{ y^{7} }} \color{purple}{\frac{\sqrt[8]{ y }}{\sqrt[8]{ y }}} \\=\frac{\sqrt[8]{ y }}{|y^{2}|}\\---------------\)
4. \(\left(q^{\frac{5}{2}}\right)^{\frac{2}{3}}\\= q^{ \frac{5}{2} . \frac{2}{3} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
5. \(\left(x^{\frac{-2}{3}}\right)^{\frac{3}{2}}\\= x^{ \frac{-2}{3} . \frac{3}{2} }= x^{-1}\\=\frac{1}{x}\\---------------\)
6. \(\left(x^{-2}\right)^{-1}\\= x^{ -2 . (-1) }= x^{2}\\\\---------------\)
7. \(\left(q^{\frac{-1}{6}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{6} . \frac{1}{3} }= q^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ q }}=\frac{1}{\sqrt[18]{ q }}. \color{purple}{\frac{\sqrt[18]{ q^{17} }}{\sqrt[18]{ q^{17} }}} \\=\frac{\sqrt[18]{ q^{17} }}{|q|}\\---------------\)
8. \(\left(a^{\frac{-5}{4}}\right)^{1}\\= a^{ \frac{-5}{4} . 1 }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
9. \(\left(a^{\frac{-2}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{-2}{3} . \frac{2}{3} }= a^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ a^{4} }}=\frac{1}{\sqrt[9]{ a^{4} }}. \color{purple}{\frac{\sqrt[9]{ a^{5} }}{\sqrt[9]{ a^{5} }}} \\=\frac{\sqrt[9]{ a^{5} }}{a}\\---------------\)
10. \(\left(q^{\frac{-5}{2}}\right)^{1}\\= q^{ \frac{-5}{2} . 1 }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
11. \(\left(a^{1}\right)^{\frac{-2}{3}}\\= a^{ 1 . (\frac{-2}{3}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
12. \(\left(x^{-1}\right)^{-2}\\= x^{ -1 . (-2) }= x^{2}\\\\---------------\)