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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-5}{6}}\right)^{\frac{3}{2}}\\= a^{ \frac{-5}{6} . \frac{3}{2} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
2. \(\left(x^{\frac{-2}{3}}\right)^{1}\\= x^{ \frac{-2}{3} . 1 }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
3. \(\left(x^{\frac{-3}{4}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-3}{4} . (\frac{-4}{5}) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
4. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-1}{3} . (\frac{-2}{3}) }= q^{\frac{2}{9}}\\=\sqrt[9]{ q^{2} }\\---------------\)
5. \(\left(a^{\frac{5}{2}}\right)^{-1}\\= a^{ \frac{5}{2} . (-1) }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
6. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-5}{6}}\\= q^{ \frac{-4}{3} . (\frac{-5}{6}) }= q^{\frac{10}{9}}\\=\sqrt[9]{ q^{10} }=q.\sqrt[9]{ q }\\---------------\)
7. \(\left(q^{\frac{5}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{5}{3} . (\frac{-1}{2}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
8. \(\left(q^{-2}\right)^{\frac{-2}{3}}\\= q^{ -2 . (\frac{-2}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
9. \(\left(y^{\frac{-3}{4}}\right)^{\frac{5}{2}}\\= y^{ \frac{-3}{4} . \frac{5}{2} }= y^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ y^{15} }}\\=\frac{1}{|y|.\sqrt[8]{ y^{7} }}=\frac{1}{|y|.\sqrt[8]{ y^{7} }} \color{purple}{\frac{\sqrt[8]{ y }}{\sqrt[8]{ y }}} \\=\frac{\sqrt[8]{ y }}{|y^{2}|}\\---------------\)
10. \(\left(q^{1}\right)^{\frac{5}{3}}\\= q^{ 1 . \frac{5}{3} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
11. \(\left(y^{1}\right)^{\frac{-4}{5}}\\= y^{ 1 . (\frac{-4}{5}) }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
12. \(\left(q^{\frac{-4}{3}}\right)^{\frac{1}{3}}\\= q^{ \frac{-4}{3} . \frac{1}{3} }= q^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ q^{4} }}=\frac{1}{\sqrt[9]{ q^{4} }}. \color{purple}{\frac{\sqrt[9]{ q^{5} }}{\sqrt[9]{ q^{5} }}} \\=\frac{\sqrt[9]{ q^{5} }}{q}\\---------------\)