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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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