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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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