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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-3}{4}}\\= a^{ \frac{-2}{5} . (\frac{-3}{4}) }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)
2. \(\left(q^{\frac{1}{3}}\right)^{2}\\= q^{ \frac{1}{3} . 2 }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
3. \(\left(a^{\frac{1}{2}}\right)^{\frac{-2}{5}}\\= a^{ \frac{1}{2} . (\frac{-2}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
4. \(\left(y^{\frac{2}{5}}\right)^{\frac{-1}{5}}\\= y^{ \frac{2}{5} . (\frac{-1}{5}) }= y^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ y^{2} }}=\frac{1}{\sqrt[25]{ y^{2} }}. \color{purple}{\frac{\sqrt[25]{ y^{23} }}{\sqrt[25]{ y^{23} }}} \\=\frac{\sqrt[25]{ y^{23} }}{y}\\---------------\)
5. \(\left(y^{1}\right)^{\frac{-3}{4}}\\= y^{ 1 . (\frac{-3}{4}) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
6. \(\left(q^{\frac{3}{2}}\right)^{1}\\= q^{ \frac{3}{2} . 1 }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
7. \(\left(q^{-1}\right)^{1}\\= q^{ -1 . 1 }= q^{-1}\\=\frac{1}{q}\\---------------\)
8. \(\left(y^{1}\right)^{\frac{-5}{6}}\\= y^{ 1 . (\frac{-5}{6}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
9. \(\left(y^{\frac{-3}{2}}\right)^{\frac{-2}{5}}\\= y^{ \frac{-3}{2} . (\frac{-2}{5}) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
10. \(\left(x^{\frac{-3}{5}}\right)^{\frac{1}{3}}\\= x^{ \frac{-3}{5} . \frac{1}{3} }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
11. \(\left(y^{\frac{-5}{4}}\right)^{\frac{1}{2}}\\= y^{ \frac{-5}{4} . \frac{1}{2} }= y^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ y^{5} }}=\frac{1}{\sqrt[8]{ y^{5} }}. \color{purple}{\frac{\sqrt[8]{ y^{3} }}{\sqrt[8]{ y^{3} }}} \\=\frac{\sqrt[8]{ y^{3} }}{|y|}\\---------------\)
12. \(\left(a^{-2}\right)^{\frac{4}{5}}\\= a^{ -2 . \frac{4}{5} }= a^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ a^{8} }}\\=\frac{1}{a.\sqrt[5]{ a^{3} }}=\frac{1}{a.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{2}}\\---------------\)