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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{4}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{4} . \frac{1}{2} }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)
2. \(\left(x^{\frac{1}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{1}{2} . (\frac{-2}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
3. \(\left(x^{\frac{-5}{2}}\right)^{\frac{-3}{5}}\\= x^{ \frac{-5}{2} . (\frac{-3}{5}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
4. \(\left(y^{\frac{-1}{2}}\right)^{1}\\= y^{ \frac{-1}{2} . 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
5. \(\left(q^{\frac{4}{3}}\right)^{-1}\\= q^{ \frac{4}{3} . (-1) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
6. \(\left(q^{1}\right)^{\frac{4}{3}}\\= q^{ 1 . \frac{4}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
7. \(\left(a^{\frac{1}{6}}\right)^{\frac{-1}{3}}\\= a^{ \frac{1}{6} . (\frac{-1}{3}) }= a^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ a }}=\frac{1}{\sqrt[18]{ a }}. \color{purple}{\frac{\sqrt[18]{ a^{17} }}{\sqrt[18]{ a^{17} }}} \\=\frac{\sqrt[18]{ a^{17} }}{|a|}\\---------------\)
8. \(\left(x^{\frac{-2}{3}}\right)^{\frac{2}{5}}\\= x^{ \frac{-2}{3} . \frac{2}{5} }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
9. \(\left(q^{\frac{1}{5}}\right)^{\frac{1}{6}}\\= q^{ \frac{1}{5} . \frac{1}{6} }= q^{\frac{1}{30}}\\=\sqrt[30]{ q }\\---------------\)
10. \(\left(q^{\frac{3}{5}}\right)^{\frac{3}{2}}\\= q^{ \frac{3}{5} . \frac{3}{2} }= q^{\frac{9}{10}}\\=\sqrt[10]{ q^{9} }\\---------------\)
11. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)
12. \(\left(x^{\frac{-1}{3}}\right)^{1}\\= x^{ \frac{-1}{3} . 1 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)