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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{1}{2}}\right)^{\frac{5}{3}}\\= a^{ \frac{1}{2} . \frac{5}{3} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
2. \(\left(y^{\frac{5}{2}}\right)^{\frac{5}{2}}\\= y^{ \frac{5}{2} . \frac{5}{2} }= y^{\frac{25}{4}}\\=\sqrt[4]{ y^{25} }=|y^{6}|.\sqrt[4]{ y }\\---------------\)
3. \(\left(x^{-1}\right)^{1}\\= x^{ -1 . 1 }= x^{-1}\\=\frac{1}{x}\\---------------\)
4. \(\left(q^{\frac{-2}{5}}\right)^{\frac{4}{5}}\\= q^{ \frac{-2}{5} . \frac{4}{5} }= q^{\frac{-8}{25}}\\=\frac{1}{\sqrt[25]{ q^{8} }}=\frac{1}{\sqrt[25]{ q^{8} }}. \color{purple}{\frac{\sqrt[25]{ q^{17} }}{\sqrt[25]{ q^{17} }}} \\=\frac{\sqrt[25]{ q^{17} }}{q}\\---------------\)
5. \(\left(y^{\frac{1}{5}}\right)^{\frac{-2}{3}}\\= y^{ \frac{1}{5} . (\frac{-2}{3}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
6. \(\left(y^{\frac{-5}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{-5}{2} . \frac{1}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
7. \(\left(x^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{3} . \frac{1}{2} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
8. \(\left(a^{\frac{3}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{3}{2} . (\frac{-1}{2}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
9. \(\left(q^{\frac{-1}{4}}\right)^{-1}\\= q^{ \frac{-1}{4} . (-1) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
10. \(\left(a^{\frac{1}{2}}\right)^{\frac{5}{4}}\\= a^{ \frac{1}{2} . \frac{5}{4} }= a^{\frac{5}{8}}\\=\sqrt[8]{ a^{5} }\\---------------\)
11. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-4}{5}}\\= q^{ \frac{-2}{5} . (\frac{-4}{5}) }= q^{\frac{8}{25}}\\=\sqrt[25]{ q^{8} }\\---------------\)
12. \(\left(a^{\frac{1}{2}}\right)^{-1}\\= a^{ \frac{1}{2} . (-1) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)