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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-1}\right)^{\frac{-3}{5}}\\= q^{ -1 . (\frac{-3}{5}) }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
2. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-5}{6}}\\= q^{ \frac{-1}{2} . (\frac{-5}{6}) }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
3. \(\left(a^{\frac{-1}{2}}\right)^{\frac{5}{6}}\\= a^{ \frac{-1}{2} . \frac{5}{6} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
4. \(\left(q^{1}\right)^{\frac{-3}{2}}\\= q^{ 1 . (\frac{-3}{2}) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
5. \(\left(y^{\frac{-5}{3}}\right)^{\frac{5}{2}}\\= y^{ \frac{-5}{3} . \frac{5}{2} }= y^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ y^{25} }}\\=\frac{1}{|y^{4}|.\sqrt[6]{ y }}=\frac{1}{|y^{4}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{5}|}\\---------------\)
6. \(\left(x^{\frac{1}{2}}\right)^{\frac{-3}{4}}\\= x^{ \frac{1}{2} . (\frac{-3}{4}) }= x^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ x^{3} }}=\frac{1}{\sqrt[8]{ x^{3} }}. \color{purple}{\frac{\sqrt[8]{ x^{5} }}{\sqrt[8]{ x^{5} }}} \\=\frac{\sqrt[8]{ x^{5} }}{|x|}\\---------------\)
7. \(\left(q^{\frac{1}{3}}\right)^{\frac{-3}{4}}\\= q^{ \frac{1}{3} . (\frac{-3}{4}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
8. \(\left(q^{\frac{1}{4}}\right)^{\frac{-3}{2}}\\= q^{ \frac{1}{4} . (\frac{-3}{2}) }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}. \color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)
9. \(\left(x^{\frac{1}{5}}\right)^{\frac{3}{5}}\\= x^{ \frac{1}{5} . \frac{3}{5} }= x^{\frac{3}{25}}\\=\sqrt[25]{ x^{3} }\\---------------\)
10. \(\left(x^{\frac{-1}{6}}\right)^{\frac{5}{6}}\\= x^{ \frac{-1}{6} . \frac{5}{6} }= x^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ x^{5} }}=\frac{1}{\sqrt[36]{ x^{5} }}. \color{purple}{\frac{\sqrt[36]{ x^{31} }}{\sqrt[36]{ x^{31} }}} \\=\frac{\sqrt[36]{ x^{31} }}{|x|}\\---------------\)
11. \(\left(y^{\frac{2}{5}}\right)^{-1}\\= y^{ \frac{2}{5} . (-1) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
12. \(\left(x^{\frac{4}{5}}\right)^{1}\\= x^{ \frac{4}{5} . 1 }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)