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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{5}{4}}\right)^{\frac{1}{3}}\\= q^{ \frac{5}{4} . \frac{1}{3} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
2. \(\left(x^{1}\right)^{\frac{-2}{3}}\\= x^{ 1 . (\frac{-2}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
3. \(\left(y^{\frac{2}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{2}{3} . \frac{1}{2} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
4. \(\left(a^{\frac{1}{3}}\right)^{\frac{4}{5}}\\= a^{ \frac{1}{3} . \frac{4}{5} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
5. \(\left(q^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{-2}{3} . \frac{1}{2} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
6. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-5}{2} . (\frac{-5}{3}) }= q^{\frac{25}{6}}\\=\sqrt[6]{ q^{25} }=|q^{4}|.\sqrt[6]{ q }\\---------------\)
7. \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{6}}\\= a^{ \frac{5}{6} . \frac{1}{6} }= a^{\frac{5}{36}}\\=\sqrt[36]{ a^{5} }\\---------------\)
8. \(\left(y^{-1}\right)^{-1}\\= y^{ -1 . (-1) }= y^{1}\\\\---------------\)
9. \(\left(a^{\frac{-1}{3}}\right)^{1}\\= a^{ \frac{-1}{3} . 1 }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
10. \(\left(a^{\frac{-3}{2}}\right)^{-1}\\= a^{ \frac{-3}{2} . (-1) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
11. \(\left(y^{\frac{5}{6}}\right)^{\frac{4}{5}}\\= y^{ \frac{5}{6} . \frac{4}{5} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
12. \(\left(y^{-1}\right)^{\frac{-2}{3}}\\= y^{ -1 . (\frac{-2}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)