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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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