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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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