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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{1}\right)^{\frac{3}{2}}\\= x^{ 1 . \frac{3}{2} }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
2. \(\left(y^{\frac{4}{3}}\right)^{\frac{-5}{4}}\\= y^{ \frac{4}{3} . (\frac{-5}{4}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
3. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-5}{6} . (\frac{-2}{3}) }= q^{\frac{5}{9}}\\=\sqrt[9]{ q^{5} }\\---------------\)
4. \(\left(x^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{3} . \frac{1}{2} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
5. \(\left(x^{\frac{1}{2}}\right)^{1}\\= x^{ \frac{1}{2} . 1 }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
6. \(\left(q^{\frac{4}{5}}\right)^{\frac{5}{6}}\\= q^{ \frac{4}{5} . \frac{5}{6} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
7. \(\left(a^{1}\right)^{\frac{-3}{5}}\\= a^{ 1 . (\frac{-3}{5}) }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
8. \(\left(x^{\frac{-3}{4}}\right)^{\frac{-2}{5}}\\= x^{ \frac{-3}{4} . (\frac{-2}{5}) }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
9. \(\left(y^{\frac{-4}{5}}\right)^{\frac{4}{5}}\\= y^{ \frac{-4}{5} . \frac{4}{5} }= y^{\frac{-16}{25}}\\=\frac{1}{\sqrt[25]{ y^{16} }}=\frac{1}{\sqrt[25]{ y^{16} }}. \color{purple}{\frac{\sqrt[25]{ y^{9} }}{\sqrt[25]{ y^{9} }}} \\=\frac{\sqrt[25]{ y^{9} }}{y}\\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{\frac{-5}{6}}\\= q^{ \frac{1}{2} . (\frac{-5}{6}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
11. \(\left(a^{\frac{-5}{2}}\right)^{\frac{5}{6}}\\= a^{ \frac{-5}{2} . \frac{5}{6} }= a^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ a^{25} }}\\=\frac{1}{|a^{2}|.\sqrt[12]{ a }}=\frac{1}{|a^{2}|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{3}|}\\---------------\)
12. \(\left(y^{-2}\right)^{\frac{1}{2}}\\= y^{ -2 . \frac{1}{2} }= y^{-1}\\=\frac{1}{y}\\---------------\)