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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{4}}\right)^{1}\\= q^{ \frac{-1}{4} . 1 }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
2. \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
3. \(\left(y^{\frac{4}{5}}\right)^{\frac{5}{4}}\\= y^{ \frac{4}{5} . \frac{5}{4} }= y^{1}\\\\---------------\)
4. \(\left(x^{\frac{-5}{6}}\right)^{\frac{1}{4}}\\= x^{ \frac{-5}{6} . \frac{1}{4} }= x^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ x^{5} }}=\frac{1}{\sqrt[24]{ x^{5} }}. \color{purple}{\frac{\sqrt[24]{ x^{19} }}{\sqrt[24]{ x^{19} }}} \\=\frac{\sqrt[24]{ x^{19} }}{|x|}\\---------------\)
5. \(\left(a^{\frac{1}{6}}\right)^{\frac{1}{5}}\\= a^{ \frac{1}{6} . \frac{1}{5} }= a^{\frac{1}{30}}\\=\sqrt[30]{ a }\\---------------\)
6. \(\left(a^{\frac{2}{3}}\right)^{\frac{-3}{5}}\\= a^{ \frac{2}{3} . (\frac{-3}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
7. \(\left(q^{\frac{-1}{3}}\right)^{\frac{3}{5}}\\= q^{ \frac{-1}{3} . \frac{3}{5} }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
8. \(\left(q^{\frac{2}{5}}\right)^{\frac{-4}{3}}\\= q^{ \frac{2}{5} . (\frac{-4}{3}) }= q^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ q^{8} }}=\frac{1}{\sqrt[15]{ q^{8} }}. \color{purple}{\frac{\sqrt[15]{ q^{7} }}{\sqrt[15]{ q^{7} }}} \\=\frac{\sqrt[15]{ q^{7} }}{q}\\---------------\)
9. \(\left(y^{-2}\right)^{\frac{5}{6}}\\= y^{ -2 . \frac{5}{6} }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
10. \(\left(y^{\frac{2}{3}}\right)^{\frac{-2}{3}}\\= y^{ \frac{2}{3} . (\frac{-2}{3}) }= y^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ y^{4} }}=\frac{1}{\sqrt[9]{ y^{4} }}. \color{purple}{\frac{\sqrt[9]{ y^{5} }}{\sqrt[9]{ y^{5} }}} \\=\frac{\sqrt[9]{ y^{5} }}{y}\\---------------\)
11. \(\left(x^{\frac{-5}{2}}\right)^{\frac{5}{4}}\\= x^{ \frac{-5}{2} . \frac{5}{4} }= x^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ x^{25} }}\\=\frac{1}{|x^{3}|.\sqrt[8]{ x }}=\frac{1}{|x^{3}|.\sqrt[8]{ x }} \color{purple}{\frac{\sqrt[8]{ x^{7} }}{\sqrt[8]{ x^{7} }}} \\=\frac{\sqrt[8]{ x^{7} }}{|x^{4}|}\\---------------\)
12. \(\left(a^{\frac{-3}{2}}\right)^{\frac{-2}{5}}\\= a^{ \frac{-3}{2} . (\frac{-2}{5}) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)