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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-5}{2}}\right)^{1}\\= q^{ \frac{-5}{2} . 1 }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
2. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-1}{2} . (\frac{-5}{2}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{\frac{3}{4}}\\= a^{ \frac{-1}{3} . \frac{3}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
4. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-4}{3} . (\frac{-4}{3}) }= a^{\frac{16}{9}}\\=\sqrt[9]{ a^{16} }=a.\sqrt[9]{ a^{7} }\\---------------\)
5. \(\left(a^{\frac{-2}{5}}\right)^{1}\\= a^{ \frac{-2}{5} . 1 }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
6. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-2}{5}}\\= y^{ \frac{-3}{5} . (\frac{-2}{5}) }= y^{\frac{6}{25}}\\=\sqrt[25]{ y^{6} }\\---------------\)
7. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-1}{2} . (\frac{-1}{4}) }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)
8. \(\left(q^{\frac{-1}{4}}\right)^{\frac{5}{4}}\\= q^{ \frac{-1}{4} . \frac{5}{4} }= q^{\frac{-5}{16}}\\=\frac{1}{\sqrt[16]{ q^{5} }}=\frac{1}{\sqrt[16]{ q^{5} }}. \color{purple}{\frac{\sqrt[16]{ q^{11} }}{\sqrt[16]{ q^{11} }}} \\=\frac{\sqrt[16]{ q^{11} }}{|q|}\\---------------\)
9. \(\left(a^{\frac{-4}{5}}\right)^{\frac{1}{2}}\\= a^{ \frac{-4}{5} . \frac{1}{2} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
10. \(\left(x^{\frac{5}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{5}{3} . (\frac{-2}{3}) }= x^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ x^{10} }}\\=\frac{1}{x.\sqrt[9]{ x }}=\frac{1}{x.\sqrt[9]{ x }} \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x^{2}}\\---------------\)
11. \(\left(x^{2}\right)^{1}\\= x^{ 2 . 1 }= x^{2}\\\\---------------\)
12. \(\left(x^{1}\right)^{\frac{4}{3}}\\= x^{ 1 . \frac{4}{3} }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)