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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{4}{3}}\right)^{\frac{-5}{3}}\\= q^{ \frac{4}{3} . (\frac{-5}{3}) }= q^{\frac{-20}{9}}\\=\frac{1}{\sqrt[9]{ q^{20} }}\\=\frac{1}{q^{2}.\sqrt[9]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[9]{ q^{2} }} \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q^{3}}\\---------------\)
2. \(\left(q^{\frac{1}{6}}\right)^{\frac{-1}{2}}\\= q^{ \frac{1}{6} . (\frac{-1}{2}) }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
3. \(\left(q^{\frac{4}{3}}\right)^{\frac{5}{6}}\\= q^{ \frac{4}{3} . \frac{5}{6} }= q^{\frac{10}{9}}\\=\sqrt[9]{ q^{10} }=q.\sqrt[9]{ q }\\---------------\)
4. \(\left(a^{-1}\right)^{-2}\\= a^{ -1 . (-2) }= a^{2}\\\\---------------\)
5. \(\left(x^{\frac{-3}{2}}\right)^{-2}\\= x^{ \frac{-3}{2} . (-2) }= x^{3}\\\\---------------\)
6. \(\left(a^{\frac{5}{4}}\right)^{2}\\= a^{ \frac{5}{4} . 2 }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
7. \(\left(y^{\frac{-1}{3}}\right)^{-1}\\= y^{ \frac{-1}{3} . (-1) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
8. \(\left(q^{1}\right)^{\frac{1}{4}}\\= q^{ 1 . \frac{1}{4} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
9. \(\left(y^{\frac{-3}{5}}\right)^{\frac{5}{2}}\\= y^{ \frac{-3}{5} . \frac{5}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
10. \(\left(q^{\frac{-5}{3}}\right)^{\frac{2}{5}}\\= q^{ \frac{-5}{3} . \frac{2}{5} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
11. \(\left(x^{\frac{5}{3}}\right)^{\frac{2}{5}}\\= x^{ \frac{5}{3} . \frac{2}{5} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
12. \(\left(a^{-1}\right)^{\frac{-1}{3}}\\= a^{ -1 . (\frac{-1}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)