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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{4}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{4} . \frac{2}{3} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
2. \(\left(y^{\frac{4}{5}}\right)^{\frac{-1}{5}}\\= y^{ \frac{4}{5} . (\frac{-1}{5}) }= y^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ y^{4} }}=\frac{1}{\sqrt[25]{ y^{4} }}. \color{purple}{\frac{\sqrt[25]{ y^{21} }}{\sqrt[25]{ y^{21} }}} \\=\frac{\sqrt[25]{ y^{21} }}{y}\\---------------\)
3. \(\left(y^{\frac{-3}{4}}\right)^{-1}\\= y^{ \frac{-3}{4} . (-1) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
4. \(\left(q^{\frac{-5}{2}}\right)^{\frac{3}{4}}\\= q^{ \frac{-5}{2} . \frac{3}{4} }= q^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ q^{15} }}\\=\frac{1}{|q|.\sqrt[8]{ q^{7} }}=\frac{1}{|q|.\sqrt[8]{ q^{7} }} \color{purple}{\frac{\sqrt[8]{ q }}{\sqrt[8]{ q }}} \\=\frac{\sqrt[8]{ q }}{|q^{2}|}\\---------------\)
5. \(\left(x^{\frac{-5}{3}}\right)^{\frac{2}{5}}\\= x^{ \frac{-5}{3} . \frac{2}{5} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
6. \(\left(a^{\frac{-3}{5}}\right)^{1}\\= a^{ \frac{-3}{5} . 1 }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
7. \(\left(y^{2}\right)^{\frac{-4}{5}}\\= y^{ 2 . (\frac{-4}{5}) }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)
8. \(\left(a^{\frac{-1}{2}}\right)^{\frac{3}{5}}\\= a^{ \frac{-1}{2} . \frac{3}{5} }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
9. \(\left(y^{\frac{3}{5}}\right)^{\frac{4}{3}}\\= y^{ \frac{3}{5} . \frac{4}{3} }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
10. \(\left(a^{\frac{2}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{2}{3} . \frac{1}{3} }= a^{\frac{2}{9}}\\=\sqrt[9]{ a^{2} }\\---------------\)
11. \(\left(x^{\frac{3}{5}}\right)^{\frac{-2}{3}}\\= x^{ \frac{3}{5} . (\frac{-2}{3}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
12. \(\left(a^{\frac{-5}{2}}\right)^{-1}\\= a^{ \frac{-5}{2} . (-1) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)