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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-1}{4} . (\frac{-1}{2}) }= x^{\frac{1}{8}}\\=\sqrt[8]{ x }\\---------------\)
2. \(\left(q^{\frac{-2}{3}}\right)^{\frac{2}{3}}\\= q^{ \frac{-2}{3} . \frac{2}{3} }= q^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ q^{4} }}=\frac{1}{\sqrt[9]{ q^{4} }}. \color{purple}{\frac{\sqrt[9]{ q^{5} }}{\sqrt[9]{ q^{5} }}} \\=\frac{\sqrt[9]{ q^{5} }}{q}\\---------------\)
3. \(\left(a^{\frac{-1}{5}}\right)^{\frac{-1}{2}}\\= a^{ \frac{-1}{5} . (\frac{-1}{2}) }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
4. \(\left(x^{\frac{4}{5}}\right)^{\frac{-3}{2}}\\= x^{ \frac{4}{5} . (\frac{-3}{2}) }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
5. \(\left(y^{\frac{3}{5}}\right)^{\frac{3}{5}}\\= y^{ \frac{3}{5} . \frac{3}{5} }= y^{\frac{9}{25}}\\=\sqrt[25]{ y^{9} }\\---------------\)
6. \(\left(q^{\frac{-2}{3}}\right)^{\frac{1}{3}}\\= q^{ \frac{-2}{3} . \frac{1}{3} }= q^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ q^{2} }}=\frac{1}{\sqrt[9]{ q^{2} }}. \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q}\\---------------\)
7. \(\left(y^{\frac{-2}{3}}\right)^{\frac{4}{5}}\\= y^{ \frac{-2}{3} . \frac{4}{5} }= y^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ y^{8} }}=\frac{1}{\sqrt[15]{ y^{8} }}. \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y}\\---------------\)
8. \(\left(a^{\frac{-2}{3}}\right)^{-1}\\= a^{ \frac{-2}{3} . (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
9. \(\left(y^{\frac{-1}{4}}\right)^{1}\\= y^{ \frac{-1}{4} . 1 }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
10. \(\left(a^{\frac{-5}{2}}\right)^{\frac{1}{2}}\\= a^{ \frac{-5}{2} . \frac{1}{2} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
11. \(\left(a^{\frac{-4}{5}}\right)^{1}\\= a^{ \frac{-4}{5} . 1 }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
12. \(\left(x^{\frac{5}{6}}\right)^{\frac{5}{4}}\\= x^{ \frac{5}{6} . \frac{5}{4} }= x^{\frac{25}{24}}\\=\sqrt[24]{ x^{25} }=|x|.\sqrt[24]{ x }\\---------------\)