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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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