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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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