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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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