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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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