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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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