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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-1}{5}}\\= a^{ \frac{-4}{5} . (\frac{-1}{5}) }= a^{\frac{4}{25}}\\=\sqrt[25]{ a^{4} }\\---------------\)
2. \(\left(a^{\frac{5}{4}}\right)^{\frac{3}{2}}\\= a^{ \frac{5}{4} . \frac{3}{2} }= a^{\frac{15}{8}}\\=\sqrt[8]{ a^{15} }=|a|.\sqrt[8]{ a^{7} }\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{\frac{3}{5}}\\= a^{ \frac{-1}{3} . \frac{3}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
4. \(\left(q^{1}\right)^{\frac{1}{2}}\\= q^{ 1 . \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
5. \(\left(y^{\frac{2}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{2}{3} . (\frac{-1}{3}) }= y^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ y^{2} }}=\frac{1}{\sqrt[9]{ y^{2} }}. \color{purple}{\frac{\sqrt[9]{ y^{7} }}{\sqrt[9]{ y^{7} }}} \\=\frac{\sqrt[9]{ y^{7} }}{y}\\---------------\)
6. \(\left(a^{\frac{-5}{4}}\right)^{\frac{1}{3}}\\= a^{ \frac{-5}{4} . \frac{1}{3} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
7. \(\left(x^{\frac{-1}{6}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-1}{6} . (\frac{-3}{2}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
8. \(\left(y^{\frac{4}{5}}\right)^{\frac{-2}{3}}\\= y^{ \frac{4}{5} . (\frac{-2}{3}) }= y^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ y^{8} }}=\frac{1}{\sqrt[15]{ y^{8} }}. \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y}\\---------------\)
9. \(\left(q^{\frac{3}{2}}\right)^{\frac{-5}{6}}\\= q^{ \frac{3}{2} . (\frac{-5}{6}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
10. \(\left(a^{\frac{1}{3}}\right)^{-2}\\= a^{ \frac{1}{3} . (-2) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
11. \(\left(y^{\frac{5}{3}}\right)^{\frac{-1}{6}}\\= y^{ \frac{5}{3} . (\frac{-1}{6}) }= y^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ y^{5} }}=\frac{1}{\sqrt[18]{ y^{5} }}. \color{purple}{\frac{\sqrt[18]{ y^{13} }}{\sqrt[18]{ y^{13} }}} \\=\frac{\sqrt[18]{ y^{13} }}{|y|}\\---------------\)
12. \(\left(y^{1}\right)^{\frac{-3}{5}}\\= y^{ 1 . (\frac{-3}{5}) }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)