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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{2}{5}}\right)^{\frac{-4}{3}}\\= a^{ \frac{2}{5} . (\frac{-4}{3}) }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
2. \(\left(q^{-2}\right)^{1}\\= q^{ -2 . 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
3. \(\left(q^{\frac{-4}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{-4}{3} . \frac{1}{2} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
4. \(\left(q^{\frac{3}{5}}\right)^{\frac{-1}{6}}\\= q^{ \frac{3}{5} . (\frac{-1}{6}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
5. \(\left(x^{\frac{1}{2}}\right)^{\frac{-3}{2}}\\= x^{ \frac{1}{2} . (\frac{-3}{2}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
6. \(\left(y^{\frac{1}{2}}\right)^{\frac{3}{5}}\\= y^{ \frac{1}{2} . \frac{3}{5} }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
7. \(\left(y^{\frac{3}{5}}\right)^{\frac{3}{4}}\\= y^{ \frac{3}{5} . \frac{3}{4} }= y^{\frac{9}{20}}\\=\sqrt[20]{ y^{9} }\\---------------\)
8. \(\left(x^{1}\right)^{\frac{1}{3}}\\= x^{ 1 . \frac{1}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
9. \(\left(a^{\frac{-3}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{-3}{2} . \frac{1}{2} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
10. \(\left(a^{\frac{-5}{2}}\right)^{-1}\\= a^{ \frac{-5}{2} . (-1) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
11. \(\left(x^{\frac{-5}{3}}\right)^{1}\\= x^{ \frac{-5}{3} . 1 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
12. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-2}{5} . (\frac{-3}{5}) }= a^{\frac{6}{25}}\\=\sqrt[25]{ a^{6} }\\---------------\)