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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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