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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{2}}\right)^{\frac{5}{6}}\\= y^{ \frac{-1}{2} . \frac{5}{6} }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
2. \(\left(x^{\frac{-5}{3}}\right)^{\frac{1}{3}}\\= x^{ \frac{-5}{3} . \frac{1}{3} }= x^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ x^{5} }}=\frac{1}{\sqrt[9]{ x^{5} }}. \color{purple}{\frac{\sqrt[9]{ x^{4} }}{\sqrt[9]{ x^{4} }}} \\=\frac{\sqrt[9]{ x^{4} }}{x}\\---------------\)
3. \(\left(q^{\frac{-4}{5}}\right)^{\frac{1}{2}}\\= q^{ \frac{-4}{5} . \frac{1}{2} }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
4. \(\left(x^{1}\right)^{\frac{-3}{2}}\\= x^{ 1 . (\frac{-3}{2}) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
5. \(\left(q^{\frac{5}{6}}\right)^{\frac{-5}{6}}\\= q^{ \frac{5}{6} . (\frac{-5}{6}) }= q^{\frac{-25}{36}}\\=\frac{1}{\sqrt[36]{ q^{25} }}=\frac{1}{\sqrt[36]{ q^{25} }}. \color{purple}{\frac{\sqrt[36]{ q^{11} }}{\sqrt[36]{ q^{11} }}} \\=\frac{\sqrt[36]{ q^{11} }}{|q|}\\---------------\)
6. \(\left(a^{2}\right)^{\frac{-1}{5}}\\= a^{ 2 . (\frac{-1}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
7. \(\left(x^{1}\right)^{\frac{-1}{2}}\\= x^{ 1 . (\frac{-1}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
8. \(\left(q^{\frac{-1}{2}}\right)^{\frac{3}{2}}\\= q^{ \frac{-1}{2} . \frac{3}{2} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
9. \(\left(a^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= a^{ \frac{-1}{2} . \frac{1}{3} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
10. \(\left(y^{2}\right)^{\frac{5}{2}}\\= y^{ 2 . \frac{5}{2} }= y^{5}\\\\---------------\)
11. \(\left(x^{\frac{5}{2}}\right)^{\frac{-5}{2}}\\= x^{ \frac{5}{2} . (\frac{-5}{2}) }= x^{\frac{-25}{4}}\\=\frac{1}{\sqrt[4]{ x^{25} }}\\=\frac{1}{|x^{6}|.\sqrt[4]{ x }}=\frac{1}{|x^{6}|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{7}|}\\---------------\)
12. \(\left(q^{\frac{3}{5}}\right)^{-2}\\= q^{ \frac{3}{5} . (-2) }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)