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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-4}{5}}\right)^{\frac{5}{4}}\\= x^{ \frac{-4}{5} . \frac{5}{4} }= x^{-1}\\=\frac{1}{x}\\---------------\)
2. \(\left(q^{\frac{3}{4}}\right)^{\frac{-5}{2}}\\= q^{ \frac{3}{4} . (\frac{-5}{2}) }= q^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ q^{15} }}\\=\frac{1}{|q|.\sqrt[8]{ q^{7} }}=\frac{1}{|q|.\sqrt[8]{ q^{7} }} \color{purple}{\frac{\sqrt[8]{ q }}{\sqrt[8]{ q }}} \\=\frac{\sqrt[8]{ q }}{|q^{2}|}\\---------------\)
3. \(\left(q^{\frac{2}{5}}\right)^{\frac{-1}{5}}\\= q^{ \frac{2}{5} . (\frac{-1}{5}) }= q^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ q^{2} }}=\frac{1}{\sqrt[25]{ q^{2} }}. \color{purple}{\frac{\sqrt[25]{ q^{23} }}{\sqrt[25]{ q^{23} }}} \\=\frac{\sqrt[25]{ q^{23} }}{q}\\---------------\)
4. \(\left(x^{\frac{1}{5}}\right)^{-2}\\= x^{ \frac{1}{5} . (-2) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
5. \(\left(a^{\frac{-1}{4}}\right)^{\frac{-5}{6}}\\= a^{ \frac{-1}{4} . (\frac{-5}{6}) }= a^{\frac{5}{24}}\\=\sqrt[24]{ a^{5} }\\---------------\)
6. \(\left(x^{\frac{-5}{2}}\right)^{\frac{1}{5}}\\= x^{ \frac{-5}{2} . \frac{1}{5} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
7. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{4}}\\= x^{ \frac{-1}{2} . \frac{1}{4} }= x^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ x }}=\frac{1}{\sqrt[8]{ x }}. \color{purple}{\frac{\sqrt[8]{ x^{7} }}{\sqrt[8]{ x^{7} }}} \\=\frac{\sqrt[8]{ x^{7} }}{|x|}\\---------------\)
8. \(\left(x^{\frac{-3}{4}}\right)^{\frac{2}{3}}\\= x^{ \frac{-3}{4} . \frac{2}{3} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
9. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-2}{5} . (\frac{-2}{3}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
10. \(\left(x^{\frac{-1}{5}}\right)^{\frac{-1}{6}}\\= x^{ \frac{-1}{5} . (\frac{-1}{6}) }= x^{\frac{1}{30}}\\=\sqrt[30]{ x }\\---------------\)
11. \(\left(x^{\frac{4}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{4}{3} . \frac{1}{2} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
12. \(\left(x^{\frac{-1}{4}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{4} . \frac{1}{2} }= x^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ x }}=\frac{1}{\sqrt[8]{ x }}. \color{purple}{\frac{\sqrt[8]{ x^{7} }}{\sqrt[8]{ x^{7} }}} \\=\frac{\sqrt[8]{ x^{7} }}{|x|}\\---------------\)