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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{3}{2}}\right)^{\frac{5}{3}}\\= x^{ \frac{3}{2} . \frac{5}{3} }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
2. \(\left(q^{1}\right)^{\frac{-2}{5}}\\= q^{ 1 . (\frac{-2}{5}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
3. \(\left(x^{\frac{-4}{3}}\right)^{\frac{3}{5}}\\= x^{ \frac{-4}{3} . \frac{3}{5} }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
4. \(\left(y^{\frac{3}{5}}\right)^{1}\\= y^{ \frac{3}{5} . 1 }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
5. \(\left(q^{\frac{1}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{3} . (\frac{-1}{3}) }= q^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ q }}=\frac{1}{\sqrt[9]{ q }}. \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q}\\---------------\)
6. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-1}{3} . (\frac{-1}{6}) }= a^{\frac{1}{18}}\\=\sqrt[18]{ a }\\---------------\)
7. \(\left(x^{\frac{-1}{6}}\right)^{\frac{3}{2}}\\= x^{ \frac{-1}{6} . \frac{3}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
8. \(\left(x^{\frac{-2}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{-2}{3} . \frac{2}{3} }= x^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ x^{4} }}=\frac{1}{\sqrt[9]{ x^{4} }}. \color{purple}{\frac{\sqrt[9]{ x^{5} }}{\sqrt[9]{ x^{5} }}} \\=\frac{\sqrt[9]{ x^{5} }}{x}\\---------------\)
9. \(\left(y^{\frac{3}{2}}\right)^{\frac{-1}{3}}\\= y^{ \frac{3}{2} . (\frac{-1}{3}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
10. \(\left(y^{\frac{5}{2}}\right)^{\frac{1}{5}}\\= y^{ \frac{5}{2} . \frac{1}{5} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
11. \(\left(a^{2}\right)^{\frac{-3}{2}}\\= a^{ 2 . (\frac{-3}{2}) }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
12. \(\left(x^{2}\right)^{\frac{5}{6}}\\= x^{ 2 . \frac{5}{6} }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)