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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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