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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{2}}\right)^{\frac{-5}{4}}\\= x^{ \frac{1}{2} . (\frac{-5}{4}) }= x^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ x^{5} }}=\frac{1}{\sqrt[8]{ x^{5} }}. \color{purple}{\frac{\sqrt[8]{ x^{3} }}{\sqrt[8]{ x^{3} }}} \\=\frac{\sqrt[8]{ x^{3} }}{|x|}\\---------------\)
2. \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{4}}\\= a^{ \frac{1}{3} . (\frac{-1}{4}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
3. \(\left(q^{-1}\right)^{\frac{3}{5}}\\= q^{ -1 . \frac{3}{5} }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
4. \(\left(a^{\frac{-5}{6}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-5}{6} . (\frac{-1}{6}) }= a^{\frac{5}{36}}\\=\sqrt[36]{ a^{5} }\\---------------\)
5. \(\left(x^{\frac{1}{3}}\right)^{-1}\\= x^{ \frac{1}{3} . (-1) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
6. \(\left(y^{\frac{1}{2}}\right)^{\frac{-2}{5}}\\= y^{ \frac{1}{2} . (\frac{-2}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
7. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-5}{2}}\\= x^{ \frac{-1}{2} . (\frac{-5}{2}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
8. \(\left(q^{\frac{-5}{4}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-5}{4} . (\frac{-1}{5}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
9. \(\left(q^{\frac{-2}{3}}\right)^{1}\\= q^{ \frac{-2}{3} . 1 }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
10. \(\left(x^{\frac{2}{3}}\right)^{\frac{1}{6}}\\= x^{ \frac{2}{3} . \frac{1}{6} }= x^{\frac{1}{9}}\\=\sqrt[9]{ x }\\---------------\)
11. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-5}{3}}\\= x^{ \frac{-5}{3} . (\frac{-5}{3}) }= x^{\frac{25}{9}}\\=\sqrt[9]{ x^{25} }=x^{2}.\sqrt[9]{ x^{7} }\\---------------\)
12. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-1}{4} . (\frac{-2}{3}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)