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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-2}{3} . (\frac{-5}{3}) }= q^{\frac{10}{9}}\\=\sqrt[9]{ q^{10} }=q.\sqrt[9]{ q }\\---------------\)
2. \(\left(a^{\frac{-5}{2}}\right)^{\frac{4}{3}}\\= a^{ \frac{-5}{2} . \frac{4}{3} }= a^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ a^{10} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a }}=\frac{1}{a^{3}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{4}}\\---------------\)
3. \(\left(a^{\frac{5}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{5}{2} . \frac{1}{2} }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
4. \(\left(q^{2}\right)^{\frac{5}{6}}\\= q^{ 2 . \frac{5}{6} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
5. \(\left(a^{-2}\right)^{\frac{1}{2}}\\= a^{ -2 . \frac{1}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
6. \(\left(q^{1}\right)^{\frac{-1}{3}}\\= q^{ 1 . (\frac{-1}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
7. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-4}{3} . (\frac{-3}{4}) }= q^{1}\\\\---------------\)
8. \(\left(q^{\frac{1}{6}}\right)^{-1}\\= q^{ \frac{1}{6} . (-1) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
9. \(\left(x^{\frac{3}{5}}\right)^{-1}\\= x^{ \frac{3}{5} . (-1) }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
10. \(\left(a^{\frac{5}{2}}\right)^{\frac{-1}{5}}\\= a^{ \frac{5}{2} . (\frac{-1}{5}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
11. \(\left(q^{\frac{1}{4}}\right)^{\frac{5}{6}}\\= q^{ \frac{1}{4} . \frac{5}{6} }= q^{\frac{5}{24}}\\=\sqrt[24]{ q^{5} }\\---------------\)
12. \(\left(y^{\frac{-3}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-3}{2} . (\frac{-1}{2}) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)