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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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