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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{2}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{2}{5} . (\frac{-1}{2}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
2. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-4}{5}}\\= a^{ \frac{-4}{3} . (\frac{-4}{5}) }= a^{\frac{16}{15}}\\=\sqrt[15]{ a^{16} }=a.\sqrt[15]{ a }\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{-1}{3} . \frac{1}{2} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
4. \(\left(a^{\frac{1}{2}}\right)^{\frac{3}{2}}\\= a^{ \frac{1}{2} . \frac{3}{2} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
5. \(\left(a^{-2}\right)^{\frac{-4}{5}}\\= a^{ -2 . (\frac{-4}{5}) }= a^{\frac{8}{5}}\\=\sqrt[5]{ a^{8} }=a.\sqrt[5]{ a^{3} }\\---------------\)
6. \(\left(q^{\frac{-1}{2}}\right)^{\frac{4}{5}}\\= q^{ \frac{-1}{2} . \frac{4}{5} }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
7. \(\left(y^{\frac{1}{2}}\right)^{\frac{-3}{4}}\\= y^{ \frac{1}{2} . (\frac{-3}{4}) }= y^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ y^{3} }}=\frac{1}{\sqrt[8]{ y^{3} }}. \color{purple}{\frac{\sqrt[8]{ y^{5} }}{\sqrt[8]{ y^{5} }}} \\=\frac{\sqrt[8]{ y^{5} }}{|y|}\\---------------\)
8. \(\left(q^{-2}\right)^{\frac{5}{6}}\\= q^{ -2 . \frac{5}{6} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
9. \(\left(y^{\frac{5}{3}}\right)^{\frac{-1}{3}}\\= y^{ \frac{5}{3} . (\frac{-1}{3}) }= y^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ y^{5} }}=\frac{1}{\sqrt[9]{ y^{5} }}. \color{purple}{\frac{\sqrt[9]{ y^{4} }}{\sqrt[9]{ y^{4} }}} \\=\frac{\sqrt[9]{ y^{4} }}{y}\\---------------\)
10. \(\left(x^{\frac{5}{2}}\right)^{\frac{-4}{3}}\\= x^{ \frac{5}{2} . (\frac{-4}{3}) }= x^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ x^{10} }}\\=\frac{1}{x^{3}.\sqrt[3]{ x }}=\frac{1}{x^{3}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{4}}\\---------------\)
11. \(\left(a^{\frac{-5}{2}}\right)^{-1}\\= a^{ \frac{-5}{2} . (-1) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
12. \(\left(q^{\frac{4}{5}}\right)^{-1}\\= q^{ \frac{4}{5} . (-1) }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)