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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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