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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-5}{2}}\right)^{\frac{3}{2}}\\= y^{ \frac{-5}{2} . \frac{3}{2} }= y^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ y^{15} }}\\=\frac{1}{|y^{3}|.\sqrt[4]{ y^{3} }}=\frac{1}{|y^{3}|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{4}|}\\---------------\)
2. \(\left(y^{\frac{1}{3}}\right)^{\frac{2}{5}}\\= y^{ \frac{1}{3} . \frac{2}{5} }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
3. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-1}{2} . (\frac{-1}{3}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
4. \(\left(a^{\frac{-4}{5}}\right)^{\frac{5}{3}}\\= a^{ \frac{-4}{5} . \frac{5}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
5. \(\left(a^{-2}\right)^{\frac{-5}{4}}\\= a^{ -2 . (\frac{-5}{4}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
6. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-1}{2} . (\frac{-1}{6}) }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
7. \(\left(y^{\frac{1}{2}}\right)^{-1}\\= y^{ \frac{1}{2} . (-1) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
8. \(\left(a^{\frac{1}{3}}\right)^{2}\\= a^{ \frac{1}{3} . 2 }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
9. \(\left(a^{-1}\right)^{\frac{-5}{6}}\\= a^{ -1 . (\frac{-5}{6}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
10. \(\left(x^{2}\right)^{\frac{-4}{5}}\\= x^{ 2 . (\frac{-4}{5}) }= x^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ x^{8} }}\\=\frac{1}{x.\sqrt[5]{ x^{3} }}=\frac{1}{x.\sqrt[5]{ x^{3} }} \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x^{2}}\\---------------\)
11. \(\left(q^{\frac{1}{3}}\right)^{\frac{-5}{6}}\\= q^{ \frac{1}{3} . (\frac{-5}{6}) }= q^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ q^{5} }}=\frac{1}{\sqrt[18]{ q^{5} }}. \color{purple}{\frac{\sqrt[18]{ q^{13} }}{\sqrt[18]{ q^{13} }}} \\=\frac{\sqrt[18]{ q^{13} }}{|q|}\\---------------\)
12. \(\left(a^{\frac{-3}{5}}\right)^{\frac{5}{2}}\\= a^{ \frac{-3}{5} . \frac{5}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)