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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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