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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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