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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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