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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{1}\right)^{\frac{-2}{5}}\\= a^{ 1 . (\frac{-2}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
2. \(\left(q^{\frac{-1}{2}}\right)^{\frac{5}{2}}\\= q^{ \frac{-1}{2} . \frac{5}{2} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
3. \(\left(x^{\frac{3}{5}}\right)^{\frac{-1}{5}}\\= x^{ \frac{3}{5} . (\frac{-1}{5}) }= x^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ x^{3} }}=\frac{1}{\sqrt[25]{ x^{3} }}. \color{purple}{\frac{\sqrt[25]{ x^{22} }}{\sqrt[25]{ x^{22} }}} \\=\frac{\sqrt[25]{ x^{22} }}{x}\\---------------\)
4. \(\left(a^{\frac{4}{3}}\right)^{\frac{-1}{4}}\\= a^{ \frac{4}{3} . (\frac{-1}{4}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
5. \(\left(y^{\frac{5}{2}}\right)^{\frac{5}{6}}\\= y^{ \frac{5}{2} . \frac{5}{6} }= y^{\frac{25}{12}}\\=\sqrt[12]{ y^{25} }=|y^{2}|.\sqrt[12]{ y }\\---------------\)
6. \(\left(a^{\frac{-4}{5}}\right)^{\frac{1}{4}}\\= a^{ \frac{-4}{5} . \frac{1}{4} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
7. \(\left(a^{\frac{1}{3}}\right)^{\frac{-3}{4}}\\= a^{ \frac{1}{3} . (\frac{-3}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
8. \(\left(a^{-1}\right)^{1}\\= a^{ -1 . 1 }= a^{-1}\\=\frac{1}{a}\\---------------\)
9. \(\left(q^{-2}\right)^{-1}\\= q^{ -2 . (-1) }= q^{2}\\\\---------------\)
10. \(\left(a^{\frac{1}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{1}{3} . (\frac{-2}{3}) }= a^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ a^{2} }}=\frac{1}{\sqrt[9]{ a^{2} }}. \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a}\\---------------\)
11. \(\left(y^{\frac{1}{5}}\right)^{\frac{-4}{5}}\\= y^{ \frac{1}{5} . (\frac{-4}{5}) }= y^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ y^{4} }}=\frac{1}{\sqrt[25]{ y^{4} }}. \color{purple}{\frac{\sqrt[25]{ y^{21} }}{\sqrt[25]{ y^{21} }}} \\=\frac{\sqrt[25]{ y^{21} }}{y}\\---------------\)
12. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-2}{3} . (\frac{-1}{5}) }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)