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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{3}}\right)^{\frac{-5}{2}}\\= a^{ \frac{1}{3} . (\frac{-5}{2}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
2. \(\left(y^{\frac{5}{3}}\right)^{-2}\\= y^{ \frac{5}{3} . (-2) }= y^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ y^{10} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y }}=\frac{1}{y^{3}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{4}}\\---------------\)
3. \(\left(q^{\frac{2}{5}}\right)^{-1}\\= q^{ \frac{2}{5} . (-1) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
4. \(\left(a^{\frac{1}{6}}\right)^{\frac{-1}{4}}\\= a^{ \frac{1}{6} . (\frac{-1}{4}) }= a^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ a }}=\frac{1}{\sqrt[24]{ a }}. \color{purple}{\frac{\sqrt[24]{ a^{23} }}{\sqrt[24]{ a^{23} }}} \\=\frac{\sqrt[24]{ a^{23} }}{|a|}\\---------------\)
5. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{1}{3} . \frac{1}{3} }= a^{\frac{1}{9}}\\=\sqrt[9]{ a }\\---------------\)
6. \(\left(q^{1}\right)^{-1}\\= q^{ 1 . (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
7. \(\left(x^{2}\right)^{\frac{1}{3}}\\= x^{ 2 . \frac{1}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
8. \(\left(x^{\frac{5}{2}}\right)^{\frac{-1}{4}}\\= x^{ \frac{5}{2} . (\frac{-1}{4}) }= x^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ x^{5} }}=\frac{1}{\sqrt[8]{ x^{5} }}. \color{purple}{\frac{\sqrt[8]{ x^{3} }}{\sqrt[8]{ x^{3} }}} \\=\frac{\sqrt[8]{ x^{3} }}{|x|}\\---------------\)
9. \(\left(x^{\frac{-3}{2}}\right)^{\frac{-5}{3}}\\= x^{ \frac{-3}{2} . (\frac{-5}{3}) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
10. \(\left(a^{1}\right)^{\frac{-3}{5}}\\= a^{ 1 . (\frac{-3}{5}) }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
11. \(\left(a^{-2}\right)^{\frac{-2}{5}}\\= a^{ -2 . (\frac{-2}{5}) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
12. \(\left(a^{\frac{-3}{2}}\right)^{\frac{-3}{4}}\\= a^{ \frac{-3}{2} . (\frac{-3}{4}) }= a^{\frac{9}{8}}\\=\sqrt[8]{ a^{9} }=|a|.\sqrt[8]{ a }\\---------------\)