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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-3}{2}}\right)^{-1}\\= y^{ \frac{-3}{2} . (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
2. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-4}{5} . (\frac{-4}{5}) }= y^{\frac{16}{25}}\\=\sqrt[25]{ y^{16} }\\---------------\)
3. \(\left(y^{\frac{3}{2}}\right)^{1}\\= y^{ \frac{3}{2} . 1 }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
4. \(\left(x^{\frac{1}{3}}\right)^{\frac{-5}{2}}\\= x^{ \frac{1}{3} . (\frac{-5}{2}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
5. \(\left(x^{\frac{-2}{3}}\right)^{\frac{1}{5}}\\= x^{ \frac{-2}{3} . \frac{1}{5} }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
6. \(\left(a^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{5} . (\frac{-1}{2}) }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
7. \(\left(x^{\frac{4}{5}}\right)^{\frac{-3}{4}}\\= x^{ \frac{4}{5} . (\frac{-3}{4}) }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
8. \(\left(a^{\frac{-4}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{-4}{3} . \frac{1}{3} }= a^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ a^{4} }}=\frac{1}{\sqrt[9]{ a^{4} }}. \color{purple}{\frac{\sqrt[9]{ a^{5} }}{\sqrt[9]{ a^{5} }}} \\=\frac{\sqrt[9]{ a^{5} }}{a}\\---------------\)
9. \(\left(a^{1}\right)^{\frac{-5}{6}}\\= a^{ 1 . (\frac{-5}{6}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
10. \(\left(y^{\frac{1}{2}}\right)^{1}\\= y^{ \frac{1}{2} . 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
11. \(\left(a^{\frac{5}{6}}\right)^{\frac{-2}{5}}\\= a^{ \frac{5}{6} . (\frac{-2}{5}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
12. \(\left(q^{\frac{1}{2}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{2} . (\frac{-1}{3}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)