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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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