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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{5}{6}}\right)^{\frac{-2}{3}}\\= y^{ \frac{5}{6} . (\frac{-2}{3}) }= y^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ y^{5} }}=\frac{1}{\sqrt[9]{ y^{5} }}. \color{purple}{\frac{\sqrt[9]{ y^{4} }}{\sqrt[9]{ y^{4} }}} \\=\frac{\sqrt[9]{ y^{4} }}{y}\\---------------\)
2. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-3}{5}}\\= q^{ \frac{-5}{2} . (\frac{-3}{5}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
3. \(\left(q^{\frac{1}{2}}\right)^{\frac{4}{5}}\\= q^{ \frac{1}{2} . \frac{4}{5} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
4. \(\left(x^{\frac{5}{4}}\right)^{\frac{3}{4}}\\= x^{ \frac{5}{4} . \frac{3}{4} }= x^{\frac{15}{16}}\\=\sqrt[16]{ x^{15} }\\---------------\)
5. \(\left(q^{\frac{-4}{5}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-4}{5} . (\frac{-2}{5}) }= q^{\frac{8}{25}}\\=\sqrt[25]{ q^{8} }\\---------------\)
6. \(\left(a^{\frac{-4}{5}}\right)^{\frac{1}{5}}\\= a^{ \frac{-4}{5} . \frac{1}{5} }= a^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ a^{4} }}=\frac{1}{\sqrt[25]{ a^{4} }}. \color{purple}{\frac{\sqrt[25]{ a^{21} }}{\sqrt[25]{ a^{21} }}} \\=\frac{\sqrt[25]{ a^{21} }}{a}\\---------------\)
7. \(\left(a^{\frac{-1}{2}}\right)^{\frac{5}{2}}\\= a^{ \frac{-1}{2} . \frac{5}{2} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
8. \(\left(y^{1}\right)^{\frac{-1}{2}}\\= y^{ 1 . (\frac{-1}{2}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
9. \(\left(a^{1}\right)^{2}\\= a^{ 1 . 2 }= a^{2}\\\\---------------\)
10. \(\left(y^{\frac{5}{3}}\right)^{\frac{-4}{3}}\\= y^{ \frac{5}{3} . (\frac{-4}{3}) }= y^{\frac{-20}{9}}\\=\frac{1}{\sqrt[9]{ y^{20} }}\\=\frac{1}{y^{2}.\sqrt[9]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[9]{ y^{2} }} \color{purple}{\frac{\sqrt[9]{ y^{7} }}{\sqrt[9]{ y^{7} }}} \\=\frac{\sqrt[9]{ y^{7} }}{y^{3}}\\---------------\)
11. \(\left(a^{\frac{1}{3}}\right)^{-1}\\= a^{ \frac{1}{3} . (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
12. \(\left(y^{\frac{1}{4}}\right)^{\frac{-3}{2}}\\= y^{ \frac{1}{4} . (\frac{-3}{2}) }= y^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ y^{3} }}=\frac{1}{\sqrt[8]{ y^{3} }}. \color{purple}{\frac{\sqrt[8]{ y^{5} }}{\sqrt[8]{ y^{5} }}} \\=\frac{\sqrt[8]{ y^{5} }}{|y|}\\---------------\)