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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{2}\right)^{\frac{-5}{6}}\\= y^{ 2 . (\frac{-5}{6}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
2. \(\left(q^{\frac{5}{6}}\right)^{\frac{5}{2}}\\= q^{ \frac{5}{6} . \frac{5}{2} }= q^{\frac{25}{12}}\\=\sqrt[12]{ q^{25} }=|q^{2}|.\sqrt[12]{ q }\\---------------\)
3. \(\left(a^{\frac{-1}{2}}\right)^{1}\\= a^{ \frac{-1}{2} . 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
4. \(\left(a^{\frac{5}{4}}\right)^{-1}\\= a^{ \frac{5}{4} . (-1) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
5. \(\left(y^{1}\right)^{\frac{5}{2}}\\= y^{ 1 . \frac{5}{2} }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
6. \(\left(q^{\frac{4}{5}}\right)^{\frac{2}{3}}\\= q^{ \frac{4}{5} . \frac{2}{3} }= q^{\frac{8}{15}}\\=\sqrt[15]{ q^{8} }\\---------------\)
7. \(\left(x^{\frac{4}{3}}\right)^{\frac{5}{2}}\\= x^{ \frac{4}{3} . \frac{5}{2} }= x^{\frac{10}{3}}\\=\sqrt[3]{ x^{10} }=x^{3}.\sqrt[3]{ x }\\---------------\)
8. \(\left(y^{1}\right)^{\frac{-3}{4}}\\= y^{ 1 . (\frac{-3}{4}) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
9. \(\left(a^{\frac{1}{6}}\right)^{\frac{-2}{5}}\\= a^{ \frac{1}{6} . (\frac{-2}{5}) }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
10. \(\left(y^{-2}\right)^{\frac{4}{5}}\\= y^{ -2 . \frac{4}{5} }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)
11. \(\left(y^{\frac{3}{2}}\right)^{\frac{1}{4}}\\= y^{ \frac{3}{2} . \frac{1}{4} }= y^{\frac{3}{8}}\\=\sqrt[8]{ y^{3} }\\---------------\)
12. \(\left(x^{\frac{-3}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{-3}{5} . \frac{2}{3} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)