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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-2}{5}}\right)^{-1}\\= y^{ \frac{-2}{5} . (-1) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
2. \(\left(a^{\frac{-4}{5}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-4}{5} . (\frac{-2}{3}) }= a^{\frac{8}{15}}\\=\sqrt[15]{ a^{8} }\\---------------\)
3. \(\left(q^{1}\right)^{2}\\= q^{ 1 . 2 }= q^{2}\\\\---------------\)
4. \(\left(q^{\frac{-2}{3}}\right)^{\frac{3}{4}}\\= q^{ \frac{-2}{3} . \frac{3}{4} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
5. \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
6. \(\left(x^{\frac{1}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{5} . \frac{1}{2} }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
7. \(\left(x^{\frac{5}{6}}\right)^{\frac{-4}{5}}\\= x^{ \frac{5}{6} . (\frac{-4}{5}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
8. \(\left(y^{1}\right)^{\frac{1}{3}}\\= y^{ 1 . \frac{1}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
9. \(\left(a^{\frac{2}{5}}\right)^{\frac{-1}{3}}\\= a^{ \frac{2}{5} . (\frac{-1}{3}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
10. \(\left(x^{\frac{2}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{2}{3} . (\frac{-1}{2}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
11. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-2}{3} . (\frac{-2}{3}) }= a^{\frac{4}{9}}\\=\sqrt[9]{ a^{4} }\\---------------\)
12. \(\left(x^{\frac{1}{2}}\right)^{\frac{1}{4}}\\= x^{ \frac{1}{2} . \frac{1}{4} }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)