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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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