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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{\frac{2}{3}}\\= q^{ 1 . \frac{2}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
2. \(\left(y^{\frac{2}{5}}\right)^{\frac{-3}{5}}\\= y^{ \frac{2}{5} . (\frac{-3}{5}) }= y^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ y^{6} }}=\frac{1}{\sqrt[25]{ y^{6} }}. \color{purple}{\frac{\sqrt[25]{ y^{19} }}{\sqrt[25]{ y^{19} }}} \\=\frac{\sqrt[25]{ y^{19} }}{y}\\---------------\)
3. \(\left(a^{2}\right)^{-1}\\= a^{ 2 . (-1) }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
4. \(\left(q^{1}\right)^{\frac{4}{3}}\\= q^{ 1 . \frac{4}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
5. \(\left(x^{1}\right)^{\frac{-1}{6}}\\= x^{ 1 . (\frac{-1}{6}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
6. \(\left(y^{\frac{-2}{5}}\right)^{\frac{5}{6}}\\= y^{ \frac{-2}{5} . \frac{5}{6} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
7. \(\left(x^{\frac{5}{2}}\right)^{\frac{3}{4}}\\= x^{ \frac{5}{2} . \frac{3}{4} }= x^{\frac{15}{8}}\\=\sqrt[8]{ x^{15} }=|x|.\sqrt[8]{ x^{7} }\\---------------\)
8. \(\left(y^{\frac{5}{6}}\right)^{\frac{-5}{2}}\\= y^{ \frac{5}{6} . (\frac{-5}{2}) }= y^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ y^{25} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y }}=\frac{1}{|y^{2}|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{3}|}\\---------------\)
9. \(\left(y^{-1}\right)^{\frac{-1}{2}}\\= y^{ -1 . (\frac{-1}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
10. \(\left(a^{\frac{-3}{5}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-3}{5} . (\frac{-1}{3}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
11. \(\left(q^{\frac{3}{2}}\right)^{\frac{-3}{4}}\\= q^{ \frac{3}{2} . (\frac{-3}{4}) }= q^{\frac{-9}{8}}\\=\frac{1}{\sqrt[8]{ q^{9} }}\\=\frac{1}{|q|.\sqrt[8]{ q }}=\frac{1}{|q|.\sqrt[8]{ q }} \color{purple}{\frac{\sqrt[8]{ q^{7} }}{\sqrt[8]{ q^{7} }}} \\=\frac{\sqrt[8]{ q^{7} }}{|q^{2}|}\\---------------\)
12. \(\left(a^{\frac{-1}{4}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-1}{4} . (\frac{-3}{2}) }= a^{\frac{3}{8}}\\=\sqrt[8]{ a^{3} }\\---------------\)