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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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