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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{3}{5}}\right)^{\frac{-5}{4}}\\= a^{ \frac{3}{5} . (\frac{-5}{4}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
2. \(\left(q^{1}\right)^{-1}\\= q^{ 1 . (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
3. \(\left(y^{\frac{-5}{2}}\right)^{\frac{3}{4}}\\= y^{ \frac{-5}{2} . \frac{3}{4} }= y^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ y^{15} }}\\=\frac{1}{|y|.\sqrt[8]{ y^{7} }}=\frac{1}{|y|.\sqrt[8]{ y^{7} }} \color{purple}{\frac{\sqrt[8]{ y }}{\sqrt[8]{ y }}} \\=\frac{\sqrt[8]{ y }}{|y^{2}|}\\---------------\)
4. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-5}{2} . (\frac{-1}{5}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
5. \(\left(a^{2}\right)^{-1}\\= a^{ 2 . (-1) }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
6. \(\left(x^{\frac{5}{3}}\right)^{\frac{1}{6}}\\= x^{ \frac{5}{3} . \frac{1}{6} }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)
7. \(\left(q^{\frac{-3}{4}}\right)^{2}\\= q^{ \frac{-3}{4} . 2 }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
8. \(\left(q^{\frac{5}{4}}\right)^{\frac{-4}{5}}\\= q^{ \frac{5}{4} . (\frac{-4}{5}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
9. \(\left(y^{\frac{-1}{4}}\right)^{-1}\\= y^{ \frac{-1}{4} . (-1) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
10. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{4}}\\= y^{ \frac{-1}{2} . \frac{1}{4} }= y^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ y }}=\frac{1}{\sqrt[8]{ y }}. \color{purple}{\frac{\sqrt[8]{ y^{7} }}{\sqrt[8]{ y^{7} }}} \\=\frac{\sqrt[8]{ y^{7} }}{|y|}\\---------------\)
11. \(\left(x^{\frac{3}{5}}\right)^{\frac{-4}{3}}\\= x^{ \frac{3}{5} . (\frac{-4}{3}) }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
12. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-1}{6} . (\frac{-2}{5}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)