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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-2}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{-2}{5} . \frac{2}{3} }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
2. \(\left(y^{\frac{-2}{3}}\right)^{\frac{3}{4}}\\= y^{ \frac{-2}{3} . \frac{3}{4} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
3. \(\left(q^{\frac{3}{2}}\right)^{2}\\= q^{ \frac{3}{2} . 2 }= q^{3}\\\\---------------\)
4. \(\left(a^{\frac{5}{2}}\right)^{\frac{4}{5}}\\= a^{ \frac{5}{2} . \frac{4}{5} }= a^{2}\\\\---------------\)
5. \(\left(a^{\frac{-5}{2}}\right)^{\frac{-5}{6}}\\= a^{ \frac{-5}{2} . (\frac{-5}{6}) }= a^{\frac{25}{12}}\\=\sqrt[12]{ a^{25} }=|a^{2}|.\sqrt[12]{ a }\\---------------\)
6. \(\left(x^{\frac{1}{3}}\right)^{\frac{-2}{5}}\\= x^{ \frac{1}{3} . (\frac{-2}{5}) }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
7. \(\left(q^{\frac{2}{5}}\right)^{\frac{1}{2}}\\= q^{ \frac{2}{5} . \frac{1}{2} }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
8. \(\left(x^{-1}\right)^{\frac{-4}{5}}\\= x^{ -1 . (\frac{-4}{5}) }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
9. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)
10. \(\left(y^{\frac{3}{5}}\right)^{\frac{-5}{6}}\\= y^{ \frac{3}{5} . (\frac{-5}{6}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
11. \(\left(a^{\frac{-3}{5}}\right)^{\frac{5}{3}}\\= a^{ \frac{-3}{5} . \frac{5}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)
12. \(\left(x^{\frac{-1}{6}}\right)^{\frac{-3}{2}}\\= x^{ \frac{-1}{6} . (\frac{-3}{2}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)