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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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