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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-1}{3} . (\frac{-3}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
2. \(\left(x^{1}\right)^{1}\\= x^{ 1 . 1 }= x^{1}\\\\---------------\)
3. \(\left(x^{\frac{3}{4}}\right)^{\frac{-4}{5}}\\= x^{ \frac{3}{4} . (\frac{-4}{5}) }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
4. \(\left(y^{\frac{5}{2}}\right)^{\frac{3}{4}}\\= y^{ \frac{5}{2} . \frac{3}{4} }= y^{\frac{15}{8}}\\=\sqrt[8]{ y^{15} }=|y|.\sqrt[8]{ y^{7} }\\---------------\)
5. \(\left(x^{\frac{1}{2}}\right)^{\frac{4}{5}}\\= x^{ \frac{1}{2} . \frac{4}{5} }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
6. \(\left(q^{-1}\right)^{\frac{-2}{5}}\\= q^{ -1 . (\frac{-2}{5}) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
7. \(\left(q^{\frac{-3}{4}}\right)^{\frac{2}{3}}\\= q^{ \frac{-3}{4} . \frac{2}{3} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
8. \(\left(y^{-1}\right)^{1}\\= y^{ -1 . 1 }= y^{-1}\\=\frac{1}{y}\\---------------\)
9. \(\left(x^{\frac{3}{5}}\right)^{\frac{-4}{5}}\\= x^{ \frac{3}{5} . (\frac{-4}{5}) }= x^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ x^{12} }}=\frac{1}{\sqrt[25]{ x^{12} }}. \color{purple}{\frac{\sqrt[25]{ x^{13} }}{\sqrt[25]{ x^{13} }}} \\=\frac{\sqrt[25]{ x^{13} }}{x}\\---------------\)
10. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{2} . \frac{1}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
11. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-1}{6}}\\= x^{ \frac{-5}{3} . (\frac{-1}{6}) }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)
12. \(\left(a^{-2}\right)^{-1}\\= a^{ -2 . (-1) }= a^{2}\\\\---------------\)