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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-1}\right)^{\frac{-5}{2}}\\= q^{ -1 . (\frac{-5}{2}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
2. \(\left(y^{-1}\right)^{\frac{5}{2}}\\= y^{ -1 . \frac{5}{2} }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
3. \(\left(x^{\frac{1}{6}}\right)^{\frac{3}{4}}\\= x^{ \frac{1}{6} . \frac{3}{4} }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)
4. \(\left(x^{\frac{4}{5}}\right)^{\frac{-2}{3}}\\= x^{ \frac{4}{5} . (\frac{-2}{3}) }= x^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ x^{8} }}=\frac{1}{\sqrt[15]{ x^{8} }}. \color{purple}{\frac{\sqrt[15]{ x^{7} }}{\sqrt[15]{ x^{7} }}} \\=\frac{\sqrt[15]{ x^{7} }}{x}\\---------------\)
5. \(\left(x^{\frac{-1}{5}}\right)^{\frac{2}{5}}\\= x^{ \frac{-1}{5} . \frac{2}{5} }= x^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ x^{2} }}=\frac{1}{\sqrt[25]{ x^{2} }}. \color{purple}{\frac{\sqrt[25]{ x^{23} }}{\sqrt[25]{ x^{23} }}} \\=\frac{\sqrt[25]{ x^{23} }}{x}\\---------------\)
6. \(\left(x^{\frac{-2}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{-2}{5} . \frac{2}{3} }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
7. \(\left(a^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= a^{ \frac{1}{2} . \frac{1}{3} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
8. \(\left(x^{2}\right)^{\frac{-1}{6}}\\= x^{ 2 . (\frac{-1}{6}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
9. \(\left(x^{\frac{1}{2}}\right)^{\frac{-4}{5}}\\= x^{ \frac{1}{2} . (\frac{-4}{5}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
10. \(\left(a^{\frac{-3}{2}}\right)^{\frac{4}{5}}\\= a^{ \frac{-3}{2} . \frac{4}{5} }= a^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ a^{6} }}\\=\frac{1}{a.\sqrt[5]{ a }}=\frac{1}{a.\sqrt[5]{ a }} \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a^{2}}\\---------------\)
11. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{3} . \frac{1}{2} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
12. \(\left(y^{\frac{2}{5}}\right)^{\frac{1}{6}}\\= y^{ \frac{2}{5} . \frac{1}{6} }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)