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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-3}{5}}\right)^{2}\\= x^{ \frac{-3}{5} . 2 }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
2. \(\left(x^{\frac{-1}{4}}\right)^{\frac{2}{3}}\\= x^{ \frac{-1}{4} . \frac{2}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
3. \(\left(a^{\frac{1}{4}}\right)^{\frac{4}{3}}\\= a^{ \frac{1}{4} . \frac{4}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
4. \(\left(a^{\frac{-3}{5}}\right)^{-1}\\= a^{ \frac{-3}{5} . (-1) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
5. \(\left(a^{\frac{-3}{5}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-3}{5} . (\frac{-5}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
6. \(\left(y^{\frac{3}{2}}\right)^{1}\\= y^{ \frac{3}{2} . 1 }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
7. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-2}{3} . (\frac{-5}{6}) }= y^{\frac{5}{9}}\\=\sqrt[9]{ y^{5} }\\---------------\)
8. \(\left(a^{\frac{1}{3}}\right)^{\frac{-4}{3}}\\= a^{ \frac{1}{3} . (\frac{-4}{3}) }= a^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ a^{4} }}=\frac{1}{\sqrt[9]{ a^{4} }}. \color{purple}{\frac{\sqrt[9]{ a^{5} }}{\sqrt[9]{ a^{5} }}} \\=\frac{\sqrt[9]{ a^{5} }}{a}\\---------------\)
9. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-2}{3} . (\frac{-1}{2}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
10. \(\left(a^{\frac{5}{6}}\right)^{\frac{-5}{4}}\\= a^{ \frac{5}{6} . (\frac{-5}{4}) }= a^{\frac{-25}{24}}\\=\frac{1}{\sqrt[24]{ a^{25} }}\\=\frac{1}{|a|.\sqrt[24]{ a }}=\frac{1}{|a|.\sqrt[24]{ a }} \color{purple}{\frac{\sqrt[24]{ a^{23} }}{\sqrt[24]{ a^{23} }}} \\=\frac{\sqrt[24]{ a^{23} }}{|a^{2}|}\\---------------\)
11. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-3}{5} . (\frac{-4}{5}) }= y^{\frac{12}{25}}\\=\sqrt[25]{ y^{12} }\\---------------\)
12. \(\left(x^{\frac{5}{6}}\right)^{2}\\= x^{ \frac{5}{6} . 2 }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)