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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-1}\right)^{\frac{5}{4}}\\= q^{ -1 . \frac{5}{4} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
2. \(\left(y^{\frac{-1}{4}}\right)^{\frac{1}{5}}\\= y^{ \frac{-1}{4} . \frac{1}{5} }= y^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ y }}=\frac{1}{\sqrt[20]{ y }}. \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y|}\\---------------\)
3. \(\left(a^{\frac{3}{2}}\right)^{\frac{-2}{3}}\\= a^{ \frac{3}{2} . (\frac{-2}{3}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
4. \(\left(x^{\frac{1}{4}}\right)^{\frac{-1}{6}}\\= x^{ \frac{1}{4} . (\frac{-1}{6}) }= x^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ x }}=\frac{1}{\sqrt[24]{ x }}. \color{purple}{\frac{\sqrt[24]{ x^{23} }}{\sqrt[24]{ x^{23} }}} \\=\frac{\sqrt[24]{ x^{23} }}{|x|}\\---------------\)
5. \(\left(a^{\frac{1}{3}}\right)^{-1}\\= a^{ \frac{1}{3} . (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
6. \(\left(a^{\frac{-1}{2}}\right)^{1}\\= a^{ \frac{-1}{2} . 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
7. \(\left(a^{\frac{-5}{2}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-5}{2} . (\frac{-4}{3}) }= a^{\frac{10}{3}}\\=\sqrt[3]{ a^{10} }=a^{3}.\sqrt[3]{ a }\\---------------\)
8. \(\left(q^{\frac{-1}{4}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{4} . \frac{1}{2} }= q^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ q }}=\frac{1}{\sqrt[8]{ q }}. \color{purple}{\frac{\sqrt[8]{ q^{7} }}{\sqrt[8]{ q^{7} }}} \\=\frac{\sqrt[8]{ q^{7} }}{|q|}\\---------------\)
9. \(\left(x^{\frac{2}{5}}\right)^{\frac{2}{5}}\\= x^{ \frac{2}{5} . \frac{2}{5} }= x^{\frac{4}{25}}\\=\sqrt[25]{ x^{4} }\\---------------\)
10. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-1}{5}}\\= y^{ \frac{-2}{3} . (\frac{-1}{5}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
11. \(\left(y^{\frac{3}{4}}\right)^{\frac{5}{4}}\\= y^{ \frac{3}{4} . \frac{5}{4} }= y^{\frac{15}{16}}\\=\sqrt[16]{ y^{15} }\\---------------\)
12. \(\left(y^{1}\right)^{\frac{1}{4}}\\= y^{ 1 . \frac{1}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)