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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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