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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{4}}\right)^{\frac{-2}{3}}\\= x^{ \frac{5}{4} . (\frac{-2}{3}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
2. \(\left(a^{1}\right)^{\frac{2}{5}}\\= a^{ 1 . \frac{2}{5} }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
3. \(\left(y^{\frac{5}{3}}\right)^{\frac{2}{5}}\\= y^{ \frac{5}{3} . \frac{2}{5} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
4. \(\left(x^{\frac{4}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{4}{3} . \frac{1}{2} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
5. \(\left(q^{\frac{1}{4}}\right)^{\frac{3}{4}}\\= q^{ \frac{1}{4} . \frac{3}{4} }= q^{\frac{3}{16}}\\=\sqrt[16]{ q^{3} }\\---------------\)
6. \(\left(q^{\frac{-4}{3}}\right)^{\frac{3}{5}}\\= q^{ \frac{-4}{3} . \frac{3}{5} }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
7. \(\left(y^{\frac{2}{3}}\right)^{\frac{3}{4}}\\= y^{ \frac{2}{3} . \frac{3}{4} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
8. \(\left(x^{\frac{-5}{4}}\right)^{\frac{-2}{5}}\\= x^{ \frac{-5}{4} . (\frac{-2}{5}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
9. \(\left(x^{\frac{4}{5}}\right)^{\frac{5}{6}}\\= x^{ \frac{4}{5} . \frac{5}{6} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
10. \(\left(x^{-1}\right)^{1}\\= x^{ -1 . 1 }= x^{-1}\\=\frac{1}{x}\\---------------\)
11. \(\left(x^{-1}\right)^{\frac{-2}{5}}\\= x^{ -1 . (\frac{-2}{5}) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
12. \(\left(q^{\frac{-5}{4}}\right)^{1}\\= q^{ \frac{-5}{4} . 1 }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)