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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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