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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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