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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{5}{2}}\right)^{\frac{-5}{6}}\\= y^{ \frac{5}{2} . (\frac{-5}{6}) }= y^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ y^{25} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y }}=\frac{1}{|y^{2}|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{3}|}\\---------------\)
2. \(\left(x^{\frac{5}{2}}\right)^{\frac{1}{3}}\\= x^{ \frac{5}{2} . \frac{1}{3} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
3. \(\left(y^{2}\right)^{\frac{5}{4}}\\= y^{ 2 . \frac{5}{4} }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
4. \(\left(y^{\frac{2}{5}}\right)^{\frac{-3}{5}}\\= y^{ \frac{2}{5} . (\frac{-3}{5}) }= y^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ y^{6} }}=\frac{1}{\sqrt[25]{ y^{6} }}. \color{purple}{\frac{\sqrt[25]{ y^{19} }}{\sqrt[25]{ y^{19} }}} \\=\frac{\sqrt[25]{ y^{19} }}{y}\\---------------\)
5. \(\left(a^{\frac{1}{3}}\right)^{\frac{-5}{3}}\\= a^{ \frac{1}{3} . (\frac{-5}{3}) }= a^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ a^{5} }}=\frac{1}{\sqrt[9]{ a^{5} }}. \color{purple}{\frac{\sqrt[9]{ a^{4} }}{\sqrt[9]{ a^{4} }}} \\=\frac{\sqrt[9]{ a^{4} }}{a}\\---------------\)
6. \(\left(a^{\frac{-4}{5}}\right)^{1}\\= a^{ \frac{-4}{5} . 1 }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
7. \(\left(y^{1}\right)^{\frac{-5}{3}}\\= y^{ 1 . (\frac{-5}{3}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
8. \(\left(y^{\frac{-3}{5}}\right)^{\frac{4}{5}}\\= y^{ \frac{-3}{5} . \frac{4}{5} }= y^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ y^{12} }}=\frac{1}{\sqrt[25]{ y^{12} }}. \color{purple}{\frac{\sqrt[25]{ y^{13} }}{\sqrt[25]{ y^{13} }}} \\=\frac{\sqrt[25]{ y^{13} }}{y}\\---------------\)
9. \(\left(a^{\frac{-1}{3}}\right)^{2}\\= a^{ \frac{-1}{3} . 2 }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
10. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-1}{2} . (\frac{-2}{3}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
11. \(\left(y^{\frac{-3}{4}}\right)^{1}\\= y^{ \frac{-3}{4} . 1 }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
12. \(\left(a^{\frac{3}{4}}\right)^{-2}\\= a^{ \frac{3}{4} . (-2) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)