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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-5}{2}}\right)^{1}\\= q^{ \frac{-5}{2} . 1 }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
2. \(\left(x^{\frac{-2}{3}}\right)^{-1}\\= x^{ \frac{-2}{3} . (-1) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
3. \(\left(y^{1}\right)^{\frac{1}{2}}\\= y^{ 1 . \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
4. \(\left(q^{\frac{5}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{5}{3} . \frac{1}{2} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
5. \(\left(q^{\frac{1}{2}}\right)^{\frac{5}{6}}\\= q^{ \frac{1}{2} . \frac{5}{6} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
6. \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{3}}\\= a^{ \frac{1}{2} . (\frac{-1}{3}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
7. \(\left(q^{\frac{4}{5}}\right)^{-1}\\= q^{ \frac{4}{5} . (-1) }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
8. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-2}{3} . (\frac{-1}{2}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
9. \(\left(y^{\frac{5}{4}}\right)^{\frac{-5}{4}}\\= y^{ \frac{5}{4} . (\frac{-5}{4}) }= y^{\frac{-25}{16}}\\=\frac{1}{\sqrt[16]{ y^{25} }}\\=\frac{1}{|y|.\sqrt[16]{ y^{9} }}=\frac{1}{|y|.\sqrt[16]{ y^{9} }} \color{purple}{\frac{\sqrt[16]{ y^{7} }}{\sqrt[16]{ y^{7} }}} \\=\frac{\sqrt[16]{ y^{7} }}{|y^{2}|}\\---------------\)
10. \(\left(q^{2}\right)^{\frac{-1}{6}}\\= q^{ 2 . (\frac{-1}{6}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
11. \(\left(y^{\frac{-5}{6}}\right)^{\frac{3}{4}}\\= y^{ \frac{-5}{6} . \frac{3}{4} }= y^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ y^{5} }}=\frac{1}{\sqrt[8]{ y^{5} }}. \color{purple}{\frac{\sqrt[8]{ y^{3} }}{\sqrt[8]{ y^{3} }}} \\=\frac{\sqrt[8]{ y^{3} }}{|y|}\\---------------\)
12. \(\left(y^{\frac{1}{2}}\right)^{\frac{-3}{5}}\\= y^{ \frac{1}{2} . (\frac{-3}{5}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)