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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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