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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-2}{3}}\right)^{-1}\\= x^{ \frac{-2}{3} . (-1) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
2. \(\left(x^{\frac{-1}{3}}\right)^{-2}\\= x^{ \frac{-1}{3} . (-2) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
3. \(\left(y^{\frac{-5}{3}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-5}{3} . (\frac{-3}{4}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
4. \(\left(y^{\frac{3}{4}}\right)^{\frac{1}{3}}\\= y^{ \frac{3}{4} . \frac{1}{3} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
5. \(\left(q^{\frac{-5}{3}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-5}{3} . (\frac{-5}{2}) }= q^{\frac{25}{6}}\\=\sqrt[6]{ q^{25} }=|q^{4}|.\sqrt[6]{ q }\\---------------\)
6. \(\left(q^{\frac{-1}{4}}\right)^{1}\\= q^{ \frac{-1}{4} . 1 }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
7. \(\left(a^{\frac{-3}{4}}\right)^{2}\\= a^{ \frac{-3}{4} . 2 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
8. \(\left(a^{\frac{-3}{2}}\right)^{\frac{5}{4}}\\= a^{ \frac{-3}{2} . \frac{5}{4} }= a^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ a^{15} }}\\=\frac{1}{|a|.\sqrt[8]{ a^{7} }}=\frac{1}{|a|.\sqrt[8]{ a^{7} }} \color{purple}{\frac{\sqrt[8]{ a }}{\sqrt[8]{ a }}} \\=\frac{\sqrt[8]{ a }}{|a^{2}|}\\---------------\)
9. \(\left(y^{\frac{1}{2}}\right)^{\frac{-4}{5}}\\= y^{ \frac{1}{2} . (\frac{-4}{5}) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
10. \(\left(q^{\frac{-3}{2}}\right)^{1}\\= q^{ \frac{-3}{2} . 1 }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
11. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)
12. \(\left(x^{-1}\right)^{\frac{2}{3}}\\= x^{ -1 . \frac{2}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)