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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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