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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{1}\right)^{\frac{5}{4}}\\= a^{ 1 . \frac{5}{4} }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
2. \(\left(a^{\frac{-1}{3}}\right)^{2}\\= a^{ \frac{-1}{3} . 2 }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
3. \(\left(y^{\frac{5}{6}}\right)^{\frac{1}{6}}\\= y^{ \frac{5}{6} . \frac{1}{6} }= y^{\frac{5}{36}}\\=\sqrt[36]{ y^{5} }\\---------------\)
4. \(\left(q^{\frac{5}{3}}\right)^{1}\\= q^{ \frac{5}{3} . 1 }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
5. \(\left(q^{1}\right)^{\frac{-3}{2}}\\= q^{ 1 . (\frac{-3}{2}) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
6. \(\left(x^{\frac{-1}{2}}\right)^{1}\\= x^{ \frac{-1}{2} . 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
7. \(\left(a^{\frac{4}{3}}\right)^{\frac{5}{3}}\\= a^{ \frac{4}{3} . \frac{5}{3} }= a^{\frac{20}{9}}\\=\sqrt[9]{ a^{20} }=a^{2}.\sqrt[9]{ a^{2} }\\---------------\)
8. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-5}{3} . (\frac{-1}{3}) }= a^{\frac{5}{9}}\\=\sqrt[9]{ a^{5} }\\---------------\)
9. \(\left(q^{\frac{-2}{5}}\right)^{2}\\= q^{ \frac{-2}{5} . 2 }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
10. \(\left(q^{\frac{1}{4}}\right)^{-1}\\= q^{ \frac{1}{4} . (-1) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
11. \(\left(y^{-1}\right)^{\frac{1}{6}}\\= y^{ -1 . \frac{1}{6} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
12. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-5}{2} . (\frac{-5}{2}) }= q^{\frac{25}{4}}\\=\sqrt[4]{ q^{25} }=|q^{6}|.\sqrt[4]{ q }\\---------------\)