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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-5}{4}}\right)^{\frac{3}{2}}\\= y^{ \frac{-5}{4} . \frac{3}{2} }= y^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ y^{15} }}\\=\frac{1}{|y|.\sqrt[8]{ y^{7} }}=\frac{1}{|y|.\sqrt[8]{ y^{7} }} \color{purple}{\frac{\sqrt[8]{ y }}{\sqrt[8]{ y }}} \\=\frac{\sqrt[8]{ y }}{|y^{2}|}\\---------------\)
2. \(\left(a^{\frac{1}{2}}\right)^{1}\\= a^{ \frac{1}{2} . 1 }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
3. \(\left(a^{\frac{5}{6}}\right)^{\frac{-4}{5}}\\= a^{ \frac{5}{6} . (\frac{-4}{5}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
4. \(\left(q^{\frac{-3}{5}}\right)^{\frac{2}{3}}\\= q^{ \frac{-3}{5} . \frac{2}{3} }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
5. \(\left(y^{\frac{1}{3}}\right)^{\frac{5}{6}}\\= y^{ \frac{1}{3} . \frac{5}{6} }= y^{\frac{5}{18}}\\=\sqrt[18]{ y^{5} }\\---------------\)
6. \(\left(y^{-1}\right)^{-1}\\= y^{ -1 . (-1) }= y^{1}\\\\---------------\)
7. \(\left(x^{\frac{-5}{4}}\right)^{\frac{5}{4}}\\= x^{ \frac{-5}{4} . \frac{5}{4} }= x^{\frac{-25}{16}}\\=\frac{1}{\sqrt[16]{ x^{25} }}\\=\frac{1}{|x|.\sqrt[16]{ x^{9} }}=\frac{1}{|x|.\sqrt[16]{ x^{9} }} \color{purple}{\frac{\sqrt[16]{ x^{7} }}{\sqrt[16]{ x^{7} }}} \\=\frac{\sqrt[16]{ x^{7} }}{|x^{2}|}\\---------------\)
8. \(\left(q^{\frac{2}{5}}\right)^{-1}\\= q^{ \frac{2}{5} . (-1) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
9. \(\left(a^{\frac{5}{6}}\right)^{\frac{-2}{5}}\\= a^{ \frac{5}{6} . (\frac{-2}{5}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
10. \(\left(x^{\frac{-5}{6}}\right)^{\frac{1}{2}}\\= x^{ \frac{-5}{6} . \frac{1}{2} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
11. \(\left(a^{\frac{-1}{2}}\right)^{1}\\= a^{ \frac{-1}{2} . 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
12. \(\left(x^{\frac{5}{4}}\right)^{\frac{-2}{5}}\\= x^{ \frac{5}{4} . (\frac{-2}{5}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)