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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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