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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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