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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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