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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{4}{3}}\right)^{-2}\\= a^{ \frac{4}{3} . (-2) }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
2. \(\left(x^{\frac{-5}{3}}\right)^{-1}\\= x^{ \frac{-5}{3} . (-1) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
3. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-5}{2}}\\= y^{ \frac{-1}{5} . (\frac{-5}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
4. \(\left(y^{\frac{5}{4}}\right)^{2}\\= y^{ \frac{5}{4} . 2 }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
5. \(\left(a^{-1}\right)^{1}\\= a^{ -1 . 1 }= a^{-1}\\=\frac{1}{a}\\---------------\)
6. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-5}{4}}\\= a^{ \frac{-1}{3} . (\frac{-5}{4}) }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
7. \(\left(y^{-1}\right)^{\frac{-1}{2}}\\= y^{ -1 . (\frac{-1}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
8. \(\left(q^{-1}\right)^{\frac{1}{2}}\\= q^{ -1 . \frac{1}{2} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
9. \(\left(x^{\frac{5}{3}}\right)^{\frac{-1}{6}}\\= x^{ \frac{5}{3} . (\frac{-1}{6}) }= x^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ x^{5} }}=\frac{1}{\sqrt[18]{ x^{5} }}. \color{purple}{\frac{\sqrt[18]{ x^{13} }}{\sqrt[18]{ x^{13} }}} \\=\frac{\sqrt[18]{ x^{13} }}{|x|}\\---------------\)
10. \(\left(y^{\frac{-2}{5}}\right)^{\frac{5}{3}}\\= y^{ \frac{-2}{5} . \frac{5}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
11. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-5}{3} . (\frac{-1}{6}) }= a^{\frac{5}{18}}\\=\sqrt[18]{ a^{5} }\\---------------\)
12. \(\left(q^{\frac{1}{2}}\right)^{\frac{-3}{2}}\\= q^{ \frac{1}{2} . (\frac{-3}{2}) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)