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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{6}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{6} . \frac{1}{2} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
2. \(\left(x^{\frac{-1}{2}}\right)^{\frac{4}{5}}\\= x^{ \frac{-1}{2} . \frac{4}{5} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
3. \(\left(q^{\frac{5}{6}}\right)^{\frac{-4}{5}}\\= q^{ \frac{5}{6} . (\frac{-4}{5}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
4. \(\left(q^{\frac{1}{2}}\right)^{\frac{-3}{4}}\\= q^{ \frac{1}{2} . (\frac{-3}{4}) }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}. \color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)
5. \(\left(a^{\frac{-1}{5}}\right)^{\frac{3}{5}}\\= a^{ \frac{-1}{5} . \frac{3}{5} }= a^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ a^{3} }}=\frac{1}{\sqrt[25]{ a^{3} }}. \color{purple}{\frac{\sqrt[25]{ a^{22} }}{\sqrt[25]{ a^{22} }}} \\=\frac{\sqrt[25]{ a^{22} }}{a}\\---------------\)
6. \(\left(q^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{2}{3} . (\frac{-1}{2}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
7. \(\left(y^{\frac{-1}{4}}\right)^{\frac{4}{5}}\\= y^{ \frac{-1}{4} . \frac{4}{5} }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
8. \(\left(y^{-1}\right)^{\frac{-5}{6}}\\= y^{ -1 . (\frac{-5}{6}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
9. \(\left(q^{\frac{-5}{6}}\right)^{2}\\= q^{ \frac{-5}{6} . 2 }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
10. \(\left(q^{\frac{-3}{2}}\right)^{\frac{5}{3}}\\= q^{ \frac{-3}{2} . \frac{5}{3} }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
11. \(\left(x^{\frac{5}{4}}\right)^{\frac{-2}{3}}\\= x^{ \frac{5}{4} . (\frac{-2}{3}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
12. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-1}{6}}\\= x^{ \frac{-1}{2} . (\frac{-1}{6}) }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)