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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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