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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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