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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-3}{2}}\right)^{\frac{5}{4}}\\= y^{ \frac{-3}{2} . \frac{5}{4} }= y^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ y^{15} }}\\=\frac{1}{|y|.\sqrt[8]{ y^{7} }}=\frac{1}{|y|.\sqrt[8]{ y^{7} }} \color{purple}{\frac{\sqrt[8]{ y }}{\sqrt[8]{ y }}} \\=\frac{\sqrt[8]{ y }}{|y^{2}|}\\---------------\)
2. \(\left(y^{\frac{5}{2}}\right)^{\frac{3}{4}}\\= y^{ \frac{5}{2} . \frac{3}{4} }= y^{\frac{15}{8}}\\=\sqrt[8]{ y^{15} }=|y|.\sqrt[8]{ y^{7} }\\---------------\)
3. \(\left(a^{-2}\right)^{\frac{3}{4}}\\= a^{ -2 . \frac{3}{4} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
4. \(\left(q^{\frac{-4}{3}}\right)^{\frac{3}{4}}\\= q^{ \frac{-4}{3} . \frac{3}{4} }= q^{-1}\\=\frac{1}{q}\\---------------\)
5. \(\left(q^{\frac{3}{2}}\right)^{\frac{-5}{6}}\\= q^{ \frac{3}{2} . (\frac{-5}{6}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
6. \(\left(a^{\frac{2}{3}}\right)^{\frac{-1}{6}}\\= a^{ \frac{2}{3} . (\frac{-1}{6}) }= a^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ a }}=\frac{1}{\sqrt[9]{ a }}. \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a}\\---------------\)
7. \(\left(q^{\frac{2}{5}}\right)^{\frac{-2}{3}}\\= q^{ \frac{2}{5} . (\frac{-2}{3}) }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
8. \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{2}}\\= a^{ \frac{5}{6} . \frac{1}{2} }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
9. \(\left(x^{1}\right)^{\frac{-1}{3}}\\= x^{ 1 . (\frac{-1}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
10. \(\left(a^{\frac{2}{5}}\right)^{\frac{1}{5}}\\= a^{ \frac{2}{5} . \frac{1}{5} }= a^{\frac{2}{25}}\\=\sqrt[25]{ a^{2} }\\---------------\)
11. \(\left(q^{\frac{-3}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{-3}{5} . \frac{1}{3} }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
12. \(\left(y^{\frac{-1}{5}}\right)^{1}\\= y^{ \frac{-1}{5} . 1 }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)