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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{\frac{-2}{3}}\\= q^{ 1 . (\frac{-2}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
2. \(\left(q^{\frac{-1}{3}}\right)^{\frac{4}{5}}\\= q^{ \frac{-1}{3} . \frac{4}{5} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
3. \(\left(a^{\frac{3}{4}}\right)^{\frac{1}{2}}\\= a^{ \frac{3}{4} . \frac{1}{2} }= a^{\frac{3}{8}}\\=\sqrt[8]{ a^{3} }\\---------------\)
4. \(\left(x^{-1}\right)^{\frac{3}{2}}\\= x^{ -1 . \frac{3}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
5. \(\left(x^{\frac{-3}{4}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-3}{4} . (\frac{-1}{4}) }= x^{\frac{3}{16}}\\=\sqrt[16]{ x^{3} }\\---------------\)
6. \(\left(a^{1}\right)^{\frac{1}{5}}\\= a^{ 1 . \frac{1}{5} }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
7. \(\left(q^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{5} . (\frac{-1}{2}) }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
8. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-3}{5}}\\= y^{ \frac{-1}{3} . (\frac{-3}{5}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
9. \(\left(x^{1}\right)^{\frac{-5}{4}}\\= x^{ 1 . (\frac{-5}{4}) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
10. \(\left(y^{-1}\right)^{1}\\= y^{ -1 . 1 }= y^{-1}\\=\frac{1}{y}\\---------------\)
11. \(\left(x^{\frac{1}{2}}\right)^{-1}\\= x^{ \frac{1}{2} . (-1) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
12. \(\left(y^{2}\right)^{\frac{4}{5}}\\= y^{ 2 . \frac{4}{5} }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)