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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{-2}\right)^{\frac{-1}{4}}\\= a^{ -2 . (\frac{-1}{4}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
2. \(\left(q^{\frac{-5}{3}}\right)^{\frac{1}{4}}\\= q^{ \frac{-5}{3} . \frac{1}{4} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
3. \(\left(q^{\frac{2}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{2}{3} . \frac{1}{2} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
4. \(\left(a^{\frac{5}{2}}\right)^{\frac{2}{3}}\\= a^{ \frac{5}{2} . \frac{2}{3} }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
5. \(\left(y^{\frac{-2}{3}}\right)^{\frac{5}{2}}\\= y^{ \frac{-2}{3} . \frac{5}{2} }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
6. \(\left(x^{\frac{1}{3}}\right)^{1}\\= x^{ \frac{1}{3} . 1 }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
7. \(\left(q^{\frac{-5}{6}}\right)^{\frac{1}{2}}\\= q^{ \frac{-5}{6} . \frac{1}{2} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
8. \(\left(x^{\frac{5}{6}}\right)^{\frac{-1}{4}}\\= x^{ \frac{5}{6} . (\frac{-1}{4}) }= x^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ x^{5} }}=\frac{1}{\sqrt[24]{ x^{5} }}. \color{purple}{\frac{\sqrt[24]{ x^{19} }}{\sqrt[24]{ x^{19} }}} \\=\frac{\sqrt[24]{ x^{19} }}{|x|}\\---------------\)
9. \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
10. \(\left(a^{2}\right)^{\frac{3}{5}}\\= a^{ 2 . \frac{3}{5} }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
11. \(\left(x^{\frac{-1}{3}}\right)^{\frac{5}{4}}\\= x^{ \frac{-1}{3} . \frac{5}{4} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
12. \(\left(q^{\frac{1}{4}}\right)^{-2}\\= q^{ \frac{1}{4} . (-2) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)