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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{3}}\right)^{\frac{1}{4}}\\= x^{ \frac{-1}{3} . \frac{1}{4} }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
2. \(\left(q^{1}\right)^{\frac{-1}{3}}\\= q^{ 1 . (\frac{-1}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
3. \(\left(q^{\frac{-1}{5}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-1}{5} . (\frac{-3}{4}) }= q^{\frac{3}{20}}\\=\sqrt[20]{ q^{3} }\\---------------\)
4. \(\left(q^{\frac{5}{4}}\right)^{1}\\= q^{ \frac{5}{4} . 1 }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
5. \(\left(y^{2}\right)^{\frac{2}{3}}\\= y^{ 2 . \frac{2}{3} }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
6. \(\left(a^{\frac{5}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{5}{2} . (\frac{-1}{2}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
7. \(\left(y^{\frac{1}{6}}\right)^{1}\\= y^{ \frac{1}{6} . 1 }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
8. \(\left(x^{\frac{-5}{4}}\right)^{\frac{4}{3}}\\= x^{ \frac{-5}{4} . \frac{4}{3} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
9. \(\left(x^{\frac{-1}{3}}\right)^{\frac{5}{3}}\\= x^{ \frac{-1}{3} . \frac{5}{3} }= x^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ x^{5} }}=\frac{1}{\sqrt[9]{ x^{5} }}. \color{purple}{\frac{\sqrt[9]{ x^{4} }}{\sqrt[9]{ x^{4} }}} \\=\frac{\sqrt[9]{ x^{4} }}{x}\\---------------\)
10. \(\left(y^{\frac{3}{2}}\right)^{\frac{-3}{5}}\\= y^{ \frac{3}{2} . (\frac{-3}{5}) }= y^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ y^{9} }}=\frac{1}{\sqrt[10]{ y^{9} }}. \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y|}\\---------------\)
11. \(\left(y^{-1}\right)^{\frac{5}{6}}\\= y^{ -1 . \frac{5}{6} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
12. \(\left(y^{\frac{-2}{5}}\right)^{\frac{5}{2}}\\= y^{ \frac{-2}{5} . \frac{5}{2} }= y^{-1}\\=\frac{1}{y}\\---------------\)