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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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