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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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